Recent changes

See the commit history of the the gitlab repository behind this website for a fine-grained log of the changes.

18 Mar 2025
files added/renewed: see gitlab repository.

• New preprint: The q-deformed random-to-random family in the Hecke algebra, joint with Sarah Brauner, Patricia Commins and Franco Saliola. Also available is a talk on this work.
• New draft: The representation theory of somewhere-to-below shuffles.
• Updated draft: Rook sums in the symmetric group algebra. Some proofs are more detailed, and some more results have been added. I hesitate to consider this finished while I am still exploring prior work.
• Errata to several new articles and books added, in particular Fulton's Young tableaux book, to Ceccherini-Silberstein/Scarabotti/Tolli on representations of symmetric groups, and to the combinatorial appendix of Green's Polynomial Representations of GL_n. The list of errata has been alphabetized for easier use.
• New talks on the hook length formula and counting tableaux and on the Naruse hook length formula.
• Minor changes to lecture notes, particularly An introduction to the symmetric group algebra, An introduction to the algebra of rings and fields, An Introduction to Algebraic Combinatorics and An Introduction to Discrete Mathematics.

24 Dec 2024
files added/renewed: see gitlab repository.

• New preprint: Monomial identities in the Weyl algebra, joint with Tom Roby, Stephan Wagner and Mei Yin. Also available are the slides of a talk on this work.
• Updated lecture notes: An introduction to the symmetric group algebra, now containing sections on the sign-twist and the dual of a representation and a proof of antipodal conjugacy.
• Updates to Math 235: Mathematical Problem Solving, Fall 2020 with a few new exercises and corrections.
• Corrections and minor updates to various texts and papers, including A Solomon Mackey formula for graded bialgebras (now accepted for publication).

9 Oct 2024
files added/renewed: see gitlab repository.

• New preprint: A Solomon Mackey formula for graded bialgebras. This is partly a paper, partly an outline of ongoing research; mor details will be added soon.
• New preprint: The diagonal derivative of a skew Schur polynomial, joint with Nazar Korniichuk, Kostiantyn Molokanov and Severyn Khomych.
• New draft: Rook sums in the symmetric group algebra. Partly an outline so far, as some of the results may see a better approach.
• New lecture notes: An introduction to the symmetric group algebra, based on a course I taught in Spring 2024. Presently, this contains the fundamentals of the representation theory of symmetric groups (Specht modules, Garnir relations, Young symmetrizers, the hook length formula, etc.). I plan to eventually include more, newer and non-standard material, but for now this is on ice as I am teaching other courses.
• New lecture notes: An Introduction to Discrete Mathematics, based on a course I taught in Winter 2024. These are mostly an improved edition of my analogous notes from Winter 2023, now formatted as a single text and amended with a few additional sections.
• The lecture notes (worksheets) for Math 235: Mathematical Problem Solving, Fall 2023 have been completed.
• Several new talks and FPSAC extended abstracts (all on the algebra page).
• Updates to Math 235: Mathematical Problem Solving, Fall 2020 with new material (on Wilson's theorem) and various corrections.
• New note: Solution to 84th Putnam contest 2023 problem B6 (a problem I proposed).
• New book review: review of Alexey A. Zaslavsky and Mikhail B. Skopenkov, Mathematics via Problems, parts 1 and 2.
• Corrections and minor updates to various texts and papers, including The Pak–Postnikov and Naruse skew hook length formulas: a new proof and The enriched q-monomial basis of the quasisymmetric functions.

29 Sep 2023
files added/renewed: see gitlab repository.

• New preprint: The Redei--Berge symmetric function of a directed graph, jointly with Richard P. Stanley. Some details will be added in the coming months.
• New preprint: The enriched q-monomial basis of the quasisymmetric functions, jointly with Ekaterina A. Vassilieva. Submitted to a journal.
• New preprint: The Pak–Postnikov and Naruse skew hook length formulas: a new proof, jointly with Nazar Korniichuk, Kostiantyn Molokanov and Severyn Khomych. Currently undergoing proofreading, soon to be posted on the arXiv.
• New preprint: Commutator nilpotency for somewhere-to-below shuffles. Feature-complete, but a generalization is in development.
• New project draft: Annihilating polynomials of Hopf algebra endomorphisms. Not a fully-fledged paper, but a survey of an ongoing project with some outlined proofs and open questions.
• New course: Math 530: Graph Theory, Spring 2023 with a textbook (An introduction to graph theory).
• New course: Math 235: Mathematical Problem Solving, Fall 2023 with worksheets (only one of them new so far, but more will come in November).
• Corrections and minor updates to various texts and papers, including An introduction to the algebra of rings and fields and Darij Grinberg and Tom Roby, Birational rowmotion on a rectangle over a noncommutative ring.

18 Mar 2023
files added/renewed: see gitlab repository.

• New course: Math 221: Discrete Mathematics, Winter 2023 with lecture notes and homework sets (contact me for solutions if you are an instructor).
• New course: Math 332: Undergraduate Abstract Algebra II, Winter 2023 with lecture notes and homework sets (contact me for solutions if you are an instructor).
• Corrections and minor updates to my Spring 2022 graph theory course, my Winter 2021 abstract algebra course and various others.
• More updates to the preprint Darij Grinberg and Nadia Lafrenière, The one-sided cycle shuffles in the symmetric group algebra. This has now been submitted to a journal as well.
• Errata to two articles by Forman added.

20 Dec 2022
files added/renewed: see gitlab repository.

• New course: Math 222: Enumerative Combinatorics, Fall 2022 with lecture notes and homework sets (contact me for solutions if you are an instructor). The notes are not identical with those of Fall 2019 (although they have a lot in common in the early chapters).
• Corrections and minor updates to my Spring 2022 graph theory course and my Spring 2021 algebraic combinatorics course.
• A new section (14) has been added to the preprint Darij Grinberg and Tom Roby, Birational rowmotion on a rectangle over a noncommutative ring.
• Significant updates to the preprint Darij Grinberg and Nadia Lafrenière, The one-sided cycle shuffles in the symmetric group algebra. This has now been submitted to the arXiv and will soon be submitted to a journal.
• New note: The entry sum of the inverse Cauchy matrix (submitted to an expository journal).
• New note: Similar matrices and equivalent polynomial matrices.
• Update to Notes on the combinatorial fundamentals of algebra (with new solved exercises).
• Minor updates to some other preprints (a few of which have gotten published).
• New talk on noncommutative birational rowmotion at MIT.

24 Aug 2022
files added/renewed: see gitlab repository.

• New course: Math 530: Graph Theory, Spring 2022 with lecture notes and homework sets (contact me for solutions if you are an instructor).
• Updates to my Spring 2017 grap theory course: Lecture 7 (on Hamiltonian paths in digraphs) and Lecture 8 (on tournaments and the Vandermonde determinant) have been now digitized and detailed. As they are self-contained, they can be read independently as expository notes.
• New preprint: Birational rowmotion on a rectangle over a noncommutative ring, jointly with Tom Roby. This has been submitted to the arXiv and to a journal.
• New note: Comments on arXiv:2105.00538v3, giving characteristic-free proofs of two isomorphisms of Schur functors. This was originally an email to the authors of arXiv:2105.00538v3, and still is not particularly detailed or streamlined.
• Added Elemente der Mathematik Problem 1414 (gcds of recursively defined sequences) with solution. A German version is also available.
• New talk: The one-sided cycle shuffles in the symmetric group algebra (Waterloo Algebraic Combinatorics Seminar). This is a combination of a survey and a research talk.
• Various corrections and minor updates (to preprints, papers, course materials and errata). In particular, Iterative properties of birational rowmotion (jointly with Tom Roby) has been corrected.
• Neue Aufgabensammlung: Deutsche AIMO 2022, Klausur 2.
• Aufgabensammlung Alternierende Summen: Aufgaben und Lösungen fortgeführt.

4 Feb 2022
files added/renewed: see gitlab repository.

• New course: Math 235: Mathematical Problem Solving, Fall 2021 with several worksheets.
• New course: Math 504: Advanced Linear Algebra, Fall 2021 with partial lecture notes.
• New preprint: The one-sided cycle shuffles in the symmetric group algebra, jointly with Nadia Lafreniére. This will soon be finished (the current version has some rough corners) and submitted.
• New preprint: On the rank of Hankel matrices over finite fields, jointly with Omesh Dhar Dwivedi.
• New preprint: The pre-Pieri rules.
• Various corrections and minor updates (to preprints, papers, course materials and errata).

28 Aug 2021
files added/renewed: see gitlab repository.

• New course: Math 701: Algebraic Combinatorics, Spring 2021 with lecture notes (complete as far as the course itself has come). The lecture notes include chapters on generating functions (including a detailed treatment of the univariate case, and a sketch of the multivariate and Laurent cases), integer partitions, permutations, alternating sums, determinants and symmetric functions (so far, mostly just the Littlewood-Richardson rule).
• New course: Math 533: Abstract Algebra I, Winter 2021 with draft lecture notes (in lecture-sized chunks; no big PDF yet).
• New preprint: On the square of the antipode in a connected filtered Hopf algebra.
• Updated The Elser nuclei sum revisited with many more results and context. An abridged version of this preprint has now been published in DMTCS.
• Updated Circumscribed quadrilaterals revisited with new results (roughly 10 new pages at the end). This was on my to-do list since 2008; I am not planning to make any further changes to the elementary geometry section in foreseeable time.
• Updated Petrie symmetric functions with a new generalization (Section 5.7).
• Updated The Pelletier--Ressayre hidden symmetry for Littlewood--Richardson coefficients with a connection to geometric crystals.
• Aufgabensammlung Einführung in algebraische Ungleichungen I fortgeführt.
• Various corrections and minor updates (to preprints, papers, course materials and errata).

10 Jan 2021
files added/renewed: see gitlab repository.

• New preprint: The Elser nuclei sum revisited.
• Neue Aufgabensammlung (teils mit Lösungen): Alternierende Summen: Aufgaben und Lösungen, geschrieben für die IMO-Vorbereitung 2021.
• Neue Aufgabensammlung (bislang nur das erste Kapitel fertig, und Lösungen unvollständig): Einführung in algebraische Ungleichungen I, geschrieben für die IMO-Vorbereitung 2021.
• The preprint The Pelletier--Ressayre hidden symmetry for Littlewood--Richardson coefficients has been updated.
• New course: Math 235: Mathematical Problem Solving, Fall 2020 with lecture notes (complete as far as the course itself has come) and solved homework sets (in the notes). The lecture notes include chapters on induction, sequences and sums, elementary number theory, the extremal and pigeonhole principles, enumerative combinatorics, invariants and monovariants.
• Various corrections and minor updates (to preprints, papers, course materials and errata).

4 Aug 2020
files added/renewed: see gitlab repository.

• New preprint: The Pelletier--Ressayre hidden symmetry for Littlewood--Richardson coefficients.
• The notes Darij Grinberg, Victor Reiner, Hopf algebras in combinatorics have been extended (with extra details and a few more exercises) and updated both here and on the arXiv. This version will also be pre-published as an Oberwolfach Preprint.
• The preprint Petrie symmetric functions has been finished and submitted.
• Another errata set.
• Various corrections and minor updates (to preprints, papers, course materials and errata).

11 Apr 2020
files added/renewed: see gitlab repository.

• A new section (6.6, about the Gessel-Reutenauer bijection) has been added to Darij Grinberg, Victor Reiner, Hopf algebras in combinatorics. The document will again be uploaded to the arXiv in the next couple weeks. Corrections and comments are more than welcome!
• New draft: Petrie symmetric functions, accompanied with a FPSAC abstract and IML talk.
• New draft: The eta-basis of QSym (very rough at the moment).
• New preprint: The Bhargava greedoid as a Gaussian elimination greedoid, accompanied with a FPSAC abstract and IML talk.
• New preprint: A greedoid and a matroid inspired by Bhargava's p-orderings (joint with Fedor Petrov), accompanied with a FPSAC abstract and IML talk.
• New note: Why Ring(A, k) / G injects into Ring(A^G, k).
• New course: Math 222: Enumerative Combinatorics, Fall 2019 with partial lecture notes and solved homework sets. The lecture notes include two complete chapters on counting and binomial coefficients, and will be continued next time I teach this class.
• New course: Math 201-003: Linear Algebra, Fall 2019 with blackboard notes and solved homework sets.
• A few more errata sets.
• Countless corrections and minor updates (to preprints, papers, course materials and errata).

13 Sep 2019
files added/renewed: essentially everything.

• This site is now available on the mirror server https://darijgrinberg.gitlab.io/ as well.
• Draft A basis for a quotient of symmetric polynomials and its accompanying FPSAC abstract updated further. Two more talks about it added.
• New note: Commutators, matrices and an identity of Copeland.
• New preprint: Alberto Dennunzio, Enrico Formenti, Darij Grinberg, Luciano Margara, Integrality of matrices, finiteness of matrix semigroups, and dynamics of linear cellular automata.
• New fragment: Alberto Dennunzio, Enrico Formenti, Darij Grinberg, Luciano Margara, On coprime characteristic polynomials over finite fields. This is (a self-contained) part of a longer joint paper that is still in the process of being written.
• A few exercises added to Darij Grinberg, Victor Reiner, Hopf algebras in combinatorics.
• New sections added in Regular elements of a ring, monic polynomials and "lcm-coprimality".
• Errata and marginalia are now on their separate page.
• A few more errata sets.
• Various corrections and minor updates.

10 Jan 2019
files added/renewed: about/cv.pdf, about/rs-long.pdf, about/rs.pdf, about/ts.pdf, about.html, algebra, algebra/algebra.html, algebra/basisquot.pdf, algebra/basisquot.tex, algebra/bisyl.pdf, algebra/bisyl.tex, algebra/diamond-talk.pdf, algebra/diamond-talk.tex, algebra/feray-errata.pdf, algebra/feray-errata.tex, algebra/fpsac19.pdf, algebra/fpsac19.tex, algebra/gzshuf2-long.pdf, algebra/gzshuf2.pdf, algebra/gzshuf2.tex, algebra/lambda.pdf, algebra/lambda.tex, algebra/lina.pdf, algebra/lina.tex, algebra/logid.pdf, algebra/logid.tex, algebra/mit2018.pdf, algebra/mit2018.tex, algebra/mlqs-long.pdf, algebra/mlqs.pdf, algebra/mlqs.zip, algebra/ncsu2018.pdf, algebra/ncsu2018.tex, algebra/pidisolift.pdf, algebra/pidisolift.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/spiral4det.pdf, algebra/spiral4det.tex, algebra/sumdet.pdf, algebra/sumdet.tex, algebra/trach.pdf, algebra/trach.tex, algebra/uconn2018.pdf, algebra/uconn2018.tex, azbincong.pdf, azbincong.tex, fleck.pdf, fleck.tex, index.html, lucascong.pdf, lucascong.tex, new.html, nogra.pdf, nogra.tex, primes2015/probs.pdf, primes2015/sols.pdf, primes2015/sols.tex, t/16f/*, t/17f/*, t/17s/*, t/18f/*, t/18s/*, t/index.html.

• The draft A basis for a quotient of symmetric polynomials has been significantly extended (and is now accompanied by a 12-page summary submitted to FPSAC and slides of two talks).
• New draft: On a double Sylvester determinant.
• Erik Aas, Darij Grinberg, Travis Scrimshaw, Multiline queues with spectral parameters has been finished (and submitted for publication).
• Notes on the combinatorial fundamentals of algebra updated again, with several new exercises in the permutations chapter. This version will probably stay unchanged for a while.
• Expanded The trace Cayley-Hamilton theorem again (with a new Section 5.7).
• Migrated my teaching materials from UMN into the teaching archive on this website.
• Various corrections and minor updates.

6 Oct 2018
files added/renewed: about/cv.pdf, about/rs-long.pdf, about/rs.pdf, about/ts.pdf, about.html, algebra/acnotes1-errata.pdf, algebra/acnotes1-errata.tex, algebra/algebra.html, algebra/basisquot.pdf, algebra/basisquot.tex, algebra/bidigare3-2015-errata.pdf, algebra/bidigare3-2015-errata.tex, algebra/briand-errata.pdf, algebra/briand-errata.tex, algebra/csm-errata.pdf, algebra/csm-errata.tex, algebra/dartmouth18.pdf, algebra/dartmouth18.tex, algebra/fleischmann-errata.pdf, algebra/fleischmann-errata.tex, algebra/gzshuf2-long.pdf, algebra/gzshuf2.pdf, algebra/gzshuf2.tex, algebra/lambda.pdf, algebra/lambda.tex, algebra/logid.pdf, algebra/logid.tex, algebra/McKayTensor-long.pdf, algebra/McKayTensor.pdf, algebra/McKayTensor.tex, algebra/mlqs-long.pdf, algebra/mlqs.pdf, algebra/mlqs.zip, algebra/ncd-errata.pdf, algebra/ncd-errata.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/seattle18.pdf, algebra/seattle18.tex, algebra/spiral4det.pdf, algebra/spiral4det.tex, algebra/subdiv-v7-long.pdf, algebra/subdiv-v7.pdf, algebra/subdiv-v7.tex, algebra/sumdet.pdf, algebra/sumdet.tex, algebra/symfuncs2017-2017july27-errata.pdf, algebra/symfuncs2017-2017july27-errata.tex, algebra/trach.pdf, algebra/trach.tex, algebra/urbana18a.pdf, algebra/urbana18a.tex, algebra/urbana18b.pdf, algebra/urbana18b.tex, azbincong.pdf, azbincong.tex, fleck.pdf, fleck.tex, index.html, lucascong.pdf, lucascong.tex, new.html, pen.txt, primes2015/probs.pdf, primes2015/sols.pdf, primes2015/sols.tex.

• New draft: A basis for a quotient of symmetric polynomials. This will eventually become at least one full-length paper.
• New note: An exercise on determinant-like sums.
• The expository Notes on the combinatorial fundamentals of algebra have been updated with a long new chapter on mathematical induction.
• Shuffle-compatible permutation statistics II: the exterior peak set has been updated. (Notice the new Question 2.51.)
• Various corrections and minor updates, new errata and new talks.

3 Jul 2018
files added/renewed: about/cv.pdf, about/rs.pdf, about/ts.pdf, algebra/algebra.html, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/diamond-talk.pdf, algebra/diamond-talk.tex, algebra/gzshuf2-long.pdf, algebra/gzshuf2.pdf, algebra/gzshuf2.tex, algebra/hannover2018.pdf, algebra/hannover2018.tex, algebra/hopf.pdf, algebra/hopf.tex, algebra/HopfComb-sols.pdf, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/linopt.pdf, algebra/linopt.tex, algebra/mlqs.pdf, algebra/mlqs.tex, algebra/preliepbw.pdf, algebra/preliepbw.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/sam-sym-errata.pdf, algebra/sam-sym-errata.tex, algebra/schur-ore.pdf, algebra/schur-ore.tex, algebra/subdiv-v7-long.pdf, algebra/subdiv-v7.pdf, algebra/subdiv-v7.tex, index.html, mrmoeb.pdf, mrmoeb.tex, new.html, primes2015/probs.pdf, primes2015/sols.pdf, primes2015/sols.tex, storrs2013.pdf, storrs2013.tex, zeckendorfBRIEF.pdf, zeckendorfBRIEF.tex, zeckendorfLONG.pdf, zeckendorfLONG.tex.

• Slides of two expository talks added.
• Shuffle-compatible permutation statistics II: the exterior peak set is now finished.
• Various corrections and minor updates, including new versions (also on the arXiv) of t-unique reductions for Mészáros's subdivision algebra and of Darij Grinberg, Victor Reiner, Hopf algebras in combinatorics.

14 Apr 2018
files added/renewed: about/cv.pdf, about/rs.pdf, about/ts.pdf, about.html, algebra, algebra/algebra.html, algebra/gzshuf2.pdf, algebra/gzshuf2.tex, algebra/HopfComb-sols.pdf, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/logid.pdf, algebra/logid.tex, algebra/mlqs.pdf, algebra/mlqs.tex, algebra/ncabel-long.pdf, algebra/ncabel.pdf, algebra/ncabel.tex, algebra/seattle18.pdf, algebra/seattle18.tex, algebra/urbana18a.pdf, algebra/urbana18a.tex, algebra/urbana18b.pdf, algebra/urbana18b.tex, index.html, lucascong.pdf, lucascong.tex, new.html, primes2015/probs.pdf, primes2015/sols.pdf, primes2015/sols.tex, zeckendorfBRIEF.pdf, zeckendorfBRIEF.tex, zeckendorfLONG.pdf, zeckendorfLONG.tex.

• New draft: Erik Aas, Darij Grinberg, Travis Scrimshaw, Multiline queues with spectral parameters. This still has a long way to go to completion.
• New draft: Darij Grinberg, Shuffle-compatible permutation statistics II: the exterior peak set. This, too, is incomplete at this point.
• Various corrections and minor updates, including new solved exercises in Notes on the combinatorial fundamentals of algebra, and a significantly improved Zeckendorf family identities generalized.

14 Jan 2018
files added/renewed: about/cv.pdf, about/photo.jpg, about/rs.pdf, about/ts.pdf, about.html, algebra/acnotes1-errata.pdf, algebra/acnotes1-errata.tex, algebra/algebra.html, algebra/bcl.pdf, algebra/bcl.tex, algebra/derivat.pdf, algebra/derivat.tex, algebra/desarmenien-mahonianmod.pdf, algebra/desarmenien-mahonianmod.tex, algebra/feray-errata.pdf, algebra/feray-errata.tex, algebra/gzshuf2.pdf, algebra/gzshuf2.tex, algebra/HopfComb-sols.pdf, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/lambda.pdf, algebra/lambda.tex, algebra/logid.pdf, algebra/logid.tex, algebra/McKayTensor-long.pdf, algebra/McKayTensor.pdf, algebra/McKayTensor.tex, algebra/ncabel-long.pdf, algebra/ncabel.pdf, algebra/ncabel.tex, algebra/pbw.pdf, algebra/pbw.tex, algebra/pbwlong.pdf, algebra/preliepbw.pdf, algebra/preliepbw.tex, algebra/r2t.pdf, algebra/r2t.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/schur-ore.pdf, algebra/schur-ore.tex, algebra/spiral4det.pdf, algebra/spiral4det.tex, algebra/subdiv-fpsac.pdf, algebra/subdiv-fpsac.src.zip, algebra/subdiv-v6.pdf, algebra/subdiv-v6.tex, algebra/subdiv-v7.pdf, algebra/subdiv-v7.tex, algebra/trach.pdf, algebra/trach.tex, azbincong.pdf, azbincong.tex, fleck.pdf, fleck.tex, index.html, lucascong.pdf, lucascong.tex, new.html, primes2015/probs.pdf, primes2015/sols.pdf, primes2015/sols.tex.

• New preprint: On binomial coefficients modulo squares of primes.
• New preprint (expository): The Lucas and Babbage congruences.
• The notes on Lambda-rings are now hosted directly on this site.
• Uploaded a re-edition (corrected and expanded with extra details) of another classical paper: Jacques Désarménien, Modulo-n study of Mahonian statistics (Étude modulo n des statistiques mahoniennes).
• Notes on the combinatorial fundamentals of algebra updated again, with half a dozen new exercises.
• Major updates (more general results) to t-unique reductions for Mészáros's subdivision algebra.
• Various corrections and minor updates. Also, errata added for a few other sources.

30 Aug 2017
files added/renewed: index.html, new.html, about.html, IntegralitySRC.zip, IntegralityBRIEF.pdf, primes2015/probs.pdf, primes2015/exe3.pdf, primes2015/exe3.tex, primes2015/kazh-exp.tex, primes2015/kazh-exp.pdf, primes2015/sols.pdf, primes2015/sols.tex, algebra/algebra.html, algebra/algebra.html, algebra/bcl.pdf, algebra/bcl.tex, algebra/caac17.pdf, algebra/caac17.tex, algebra/cartier-errata.pdf, algebra/cartier-errata.tex, algebra/cherednik-errata.pdf, algebra/cherednik-errata.tex, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/cornell-feb17.pdf, algebra/cornell-feb17.tex, algebra/counterMO84345.pdf, algebra/counterMO84345.tex, algebra/dgi-errata1.pdf, algebra/dgi-errata1.tex, algebra/dkr1978.pdf, algebra/dkr1978.tex, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/dp-abstr-long.pdf, algebra/fpsac2017.pdf, algebra/fpsac2017.tex, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/HopfComb-sols.pdf, algebra/kazh-gen.pdf, algebra/kazh-gen.tex, algebra/linopt.pdf, algebra/linopt.tex, algebra/logid.pdf, algebra/logid.tex, algebra/madison17.pdf, algebra/madison17.tex, algebra/McKayTensor.pdf, algebra/McKayTensor.tex, algebra/McKayTensor-long.pdf, algebra/ncabel.pdf, algebra/ncabel.tex, algebra/ncabel-long.pdf, algebra/ncd-errata.pdf, algebra/ncd-errata.tex, algebra/r2t.pdf, algebra/r2t.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/schrijver-cco-errata-2017mar23.pdf, algebra/schrijver-cco-errata-2017mar23.tex, algebra/schur-ore.pdf, algebra/schur-ore.tex, algebra/stanley-ac-errata-1.pdf, algebra/stanley-ac-errata-1.tex, algebra/subdiv-v6.pdf, algebra/subdiv-v6.tex, algebra/tensorext.pdf, algebra/tensorext.tex, algebra/thwitt-errata.pdf, algebra/thwitt-errata.tex, algebra/trach.pdf, algebra/trach.tex, algebra/va3.pdf, algebra/va3.tex, algebra/witt3.pdf, algebra/witt4.pdf, algebra/witt4b.pdf, algebra/witt5.pdf, algebra/witt5a.pdf, algebra/witt5b.pdf, algebra/witt5c.pdf, algebra/witt5d.pdf, algebra/witt5e.pdf, algebra/witt5f.pdf, algebra/wittsrc.zip, about/cv.pdf, about/rs.pdf, about/ts.pdf.

• New preprint: Darij Grinberg, Jia Huang, Victor Reiner, Critical groups for Hopf algebra modules.
• New preprint: t-unique reductions for Mészáros's subdivision algebra.
• New preprint: Noncommutative Abel-like identities.
• New class materials added: Math 5707 (Graph Theory). This includes LaTeXed notes to a few lectures, handwritten notes to a few more lectures, and various exercises with solutions by myself and by students.
• New Section 1.7 (about Leray's theorem) added to Darij Grinberg, Victor Reiner, Hopf algebras in combinatorics.
• Uploaded some "expository" notes from my grad-student days:
  • On the logarithm of the identity on connected filtered bialgebras;
  • Elementary derivations of some results of linear optimization,
  Caveat: I have written them for myself to record the proofs; they are neither well-motivated nor fun to read.
• Some new talks and errata.
• Uploaded a re-edition (corrected and expanded with extra details) of a classical paper on invariant theory: J. Désarménien, Joseph P. S. Kung, Gian-Carlo Rota, Invariant Theory, Young Bitableaux, and Combinatorics.
• New sections added in Regular elements of a ring, monic polynomials and "lcm-coprimality".
• Notes on the combinatorial fundamentals of algebra updated again, with half a dozen new exercises.
• Added PRIMES 2015 reading project: Problem set #3 (on request).
• Minor errors corrected in various notes.

27 Jan 2017
files added/renewed: index.html, new.html, maxperm.pdf, maxperm.tex, primes2015/sols.pdf, primes2015/sols.tex, primes2015/probs.pdf, algebra/algebra.html, algebra/dgi-errata1.pdf, algebra/dgi-errata1.tex, algebra/caac17.pdf, algebra/caac17.tex, algebra/cherednik-errata.pdf, algebra/cherednik-errata.tex, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/HopfComb-sols.pdf, algebra/kazh-gen.pdf, algebra/kazh-gen.tex, algebra/trach.pdf, algebra/trach.tex, algebra/ncd-errata.pdf, algebra/ncd-errata.tex, algebra/schur-ore.pdf, algebra/schur-ore.tex, algebra/KP-errata-web.pdf, algebra/KP-errata-web.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/ppoly-prob.pdf, algebra/ppoly-prob.tex, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/dp-abstr-long.pdf, algebra/fpsac2017.pdf, algebra/fpsac2017.pdf, algebra/ncg1-errata1.pdf, algebra/ncg1-errata1.tex, algebra/bcl.pdf, algebra/bcl.tex, algebra/orzech.pdf, algebra/orzech.tex

• Added an extended abstract of the preprint Double posets and the antipode of QSym. Also, updated the preprint itself with a few new minor observations and more detailed proofs.
• Added talk slides about the draft Do the symmetric functions have a function-field analogue?.
• Some new sets of errata.
• Updates to many notes and papers, most importantly to Hopf algebras in combinatorics (two new exercises added at the end of Section 2; some errors have been corrected in Section 7).

4 Nov 2016
files added/renewed: index.html, new.html, primes2015/sols.pdf, primes2015/sols.tex, primes2015/probs.pdf, algebra/schur-ore.tex, algebra/schur-ore.pdf, algebra/carlitz-status-v3.pdf (deleted), algebra/carlitz-status-v3.tex (deleted), algebra/regpol.tex, algebra/regpol.pdf, algebra/ppoly-prob.tex, algebra/ppoly-prob.pdf, algebra/trach.tex, algebra/trach.pdf, algebra/october06.tex, algebra/october06.pdf, algebra/HopfComb-sols.pdf, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/dp-abstr.tex, algebra/dp-abstr.pdf, algebra/dp-abstr-long.pdf, algebra/KP-errata-web.tex, algebra/KP-errata-web.pdf

• New expository note: On p-polynomials and F_p-vector subspaces of fields.
• Notes on the combinatorial fundamentals of algebra updated again, with a new exercise (Exercise 52, with various related results proved in the solutions section).
• New slides: Sign functions for reduced expressions in Coxeter groups: proof of a conjecture of Bergeron, Ceballos and Labbé.
• Notes on linear algebra have been abandoned for the time being, as I am short on time. The material they currently cover includes matrix operations (multiplication etc.) and various properties of matrices (triangular, invertible, permutation) as well as some basics of vector spaces. I plan to resume writing them eventually!
• The draft report Do the symmetric functions have a function-field analogue? has been further updated, with numerous proofs (although of rather elementary results -- the interesting parts are yet to come...). Furthermore, the files for this report have been renamed (carlitz-status-v3.* --> schur-ore.*), and a github repository has been created.
• Minor updates and corrections to various writings, including Double posets and the antipode of QSym (which now has a Github repository as well) and Hopf algebras in combinatorics.

25 Sep 2016
files added/renewed: index.html, new.html, about.html, algebra/algebra.html, algebra/cmc-errata1.pdf, algebra/cmc-errata1.tex, algebra/carlitz-status-v3.pdf, algebra/carlitz-status-v3.tex, algebra/trach.pdf, algebra/trach.tex, algebra/r2t.pdf, algebra/r2t.tex, algebra/HopfComb-sols.pdf, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/bcl.pdf, algebra/bcl.tex,

• Notes on linear algebra started.
• Notes on the combinatorial fundamentals of algebra updated again, with several new exercises.
• Draft Do the symmetric functions have a function-field analogue? updated again. The really interesting parts are still to come....
• Expanded The trace Cayley-Hamilton theorem again.
• Expanded Proof of a conjecture of Bergeron, Ceballos and Labbé; two conjectures are now included.
• Minor corrections and updates, including Hopf algebras in combinatorics.

20 Jul 2016
files added/renewed: index.html, new.html, algebra/algebra.html, algebra/trach.tex, algebra/trach.pdf, algebra/witt5.pdf, algebra/witt5d.pdf, algebra/witt5e.pdf, algebra/wittsrc.zip, algebra/preliepbw.tex, algebra/preliepbw.pdf, algebra/carlitz-status-v3.pdf, algebra/carlitz-status-v3.tex, primes2015/sols.pdf, primes2015/sols.tex, primes2015/probs.pdf

• Expanded The trace Cayley-Hamilton theorem.
• Minor corrections.

30 Jun 2016
files added/renewed: index.html, new.html, algebra/algebra.html, algebra/trach.tex, algebra/trach.pdf

• Added new note: The trace Cayley-Hamilton theorem.

27 Jun 2016
files added/renewed: index.html, new.html, algebra/algebra.html, algebra/kazh-gen.tex, algebra/kazh-gen.pdf, algebra/orzech.tex, algebra/orzech.pdf

• Added new preprint: Darij Grinberg, Karthik Karnik, Anya Zhang, A generalization of Chio Pivotal Condensation.
• Various corrections in A constructive proof of Orzech's theorem.

23 Jun 2016
files added/renewed: index.html, new.html, about.html, QEDMO4P13.pdf, QEDMOSRC.zip, AMMSRC.zip, AMM11403.pdf, 11403.pdf, perlen.pdf, perlen.tex, floor.pdf, floor.tex, algebra/HopfComb.tex, algebra/HopfComb.pdf, algebra/HopfComb-sols.pdf, algebra/groth1.pdf, algebra/groth1.tex, algebra/groth1alt.pdf, algebra/groth1alt.tex, algebra/regpol.pdf, algebra/regpol.tex, algebra/derivat.pdf, algebra/derivat.tex, algebra/algebra.html, algebra/quaternion.pdf, algebra/quaternion.tex, algebra/witt0.pdf, algebra/witt3.pdf, algebra/witt5.pdf, algebra/witt5b.pdf, algebra/witt5c.pdf, algebra/witt5e.pdf, algebra/witt5f.pdf, algebra/wittsrc.zip, algebra/chevalley.pdf, algebra/chevalleys.pdf, algebra/chevalleySRC.zip, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, primes2015/kazh-exp.tex, primes2015/kazh-exp.pdf, Dreigeom/QEDMO6P4deu.pdf, Dreigeom/index.html,

• New note: Regular elements of a ring, monic polynomials and "lcm-coprimality".
• Notes on the combinatorial fundamentals of algebra updated again, with two new Exercises 1 and 2 and a restructured Section 2.1 (also, Chapter 2, which had no business being at the beginning of the notes, has been moved to the end).
• Notes on Lambda-rings have been extended by a few new exercises, and corrected in various places. More importantly, the proof of Theorem 4.2 should now be readable...
• Hopf algebras in combinatorics now has an appendix explaining some linear-algebraic folklore used in the proofs (triangular matrices with respect to a partial order).
• 4th QEDMO, Problem 13 no longer has the unnecessary condition k ≤ n.
• 18.781 (Spring 2016): Floor and arithmetic functions now includes a proof of the Bezout identity for integers.
• Various minor corrections and updates.
• 1/n Summe von φ(d) q^n/d über alle d | n jetzt auch mit Sourcecode.

19 May 2016
files added/renewed: index.html, new.html, algebra/algebra.html, algebra/hgk3-errata.pdf, algebra/hgk3-errata.tex, algebra/thwitt-errata.pdf, algebra/thwitt-errata.tex, algebra/derivat.pdf, algebra/derivat.tex, algebra/bernsteinproof.tex, algebra/bernsteinproof.pdf, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/dp-abstr-long.pdf, algebra/dimcreation.pdf, algebra/dimcreation.tex, algebra/dimcreation-long.pdf, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, floor.pdf, floor.tex, fleck.pdf, fleck.tex,

• Notes on the combinatorial fundamentals of algebra (formerly known as PRIMES 2015 reading project: problems and solutions) updated with new Sections 6.18 and 6.19, new exercises and various corrections.
• Errata to Richard G. Swan, On the straightening law for minors of a matrix obsoleted, after Richard Swan has corrected the typos.
• Two new sets of errata: to Michiel Hazewinkel, Nadiya Gubareni, V. V. Kirichenko, Algebras, Rings and Modules: Lie Algebras and Hopf Algebras, and to Joseph Rabinoff, The Theory of Witt Vectors.
• Various other corrections and updates.

18 Apr 2016
files added/renewed: index.html, new.html, algebra/algebra.html, algebra/bernsteinproof.tex, algebra/bernsteinproof.pdf, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/dp-abstr-long.pdf, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/dimcreation.pdf, algebra/dimcreation.tex, algebra/dimcreation-long.pdf, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf,

• Various corrections and updates; three preprints updated in particular (also on arXiv).

14 Apr 2016
files added/renewed: index.html, new.html, floor.tex, floor.pdf, algebra/algebra.html, algebra/bernsteinproof.tex, algebra/bernsteinproof.pdf, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/dp-abstr-long.pdf, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/brandeis06.pdf, algebra/brandeis06.tex, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf,

• New note: 18.781 (Spring 2016): Floor and arithmetic functions.
• Minor corrections and updates.

10 Apr 2016 (3)
files added/renewed: index.html, new.html, algebra/algebra.html, algebra/lrrule-errata.pdf, algebra/lrrule-errata.tex, algebra/str-errata.pdf, algebra/str-errata.tex, algebra/bernsteinproof.tex, algebra/bernsteinproof.pdf,

• More errata.
• Minor corrections and updates.

10 Apr 2016 (2)
files added/renewed: index.html, new.html, fleck.tex, fleck.pdf, algebra/algebra.html, algebra/semigroups-errata-long.tex, algebra/semigroups-errata-long.pdf, algebra/semring-errata.tex, algebra/semring-errata.pdf, algebra/brandeis06.pdf, algebra/brandeis06.tex, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/dimcreation.tex, algebra/dimcreation.pdf, algebra/dimcreation-long.pdf, O111.pdf, O219.pdf, MRSRC.zip,

• Talk slides Three etudes on quasisymmetric functions. finished.
• More errata.
• Minor corrections and updates.

10 Apr 2016
files added/renewed: index.html, new.html, fleck.tex, fleck.pdf, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, algebra/algebra.html, algebra/dp-abstr.tex, algebra/dp-abstr.pdf, algebra/dp-abstr-long.pdf, algebra/bernsteinproof.pdf, algebra/bernsteinproof.tex, algebra/brandeis06.pdf, algebra/brandeis06.tex, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/preliepbw.tex, algebra/preliepbw.pdf,

• New note: Fleck's binomial congruence using circulant matrices.
• New talk slides: Three etudes on quasisymmetric functions. Only two of these etudes (Chapters 1 and 2) are finished so far.
• Minor corrections and updates.

5 Apr 2016
files added/renewed: index.html, new.html, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, algebra/algebra.html, algebra/tensorext.pdf, algebra/tensorext.tex, algebra/dp-abstr.tex, algebra/dp-abstr.pdf, algebra/dp-abstr-long.pdf, about/cv.pdf, about/rs.pdf, about/ts.pdf, algebra/bernsteinproof.pdf, algebra/bernsteinproof.tex, algebra/brandeis06.pdf, algebra/brandeis06.tex, algebra/chromatic.pdf, algebra/chromatic.tex, algebra/quaternion.pdf, algebra/quaternion.tex,

• New preprint: The Bernstein homomorphism via Aguiar-Bergeron-Sottile universality.
• Minor corrections and updates.

23 Mar 2016
files added/renewed: index.html, new.html, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, algebra/algebra.html, algebra/tensorext.pdf, algebra/tensorext.tex, algebra/dp-abstr.tex, algebra/dp-abstr.pdf, algebra/dp-abstr-long.pdf.

• Minor corrections and updates, particularly in Double posets and the antipode of QSym.

20 Mar 2016
files added/renewed: index.html, new.html, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, algebra/chromatic.tex, algebra/chromatic.pdf, algebra/dp-abstr-long.pdf, algebra/dp-abstr.tex, algebra/dp-abstr.pdf, algebra/algebra.html

• Note A note on non-broken-circuit sets and the chromatic polynomial finished.
• Minor corrections and updates. In particular, PRIMES 2015 has been renamed and updated with a new section on sums.

9 Mar 2016
files added/renewed: about/rs.pdf, about/cv.pdf, pen.txt, new.html, index.html, about.html, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf, primes2015/kazh-exp.pdf, primes2015/kazh-exp.tex, algebra/carlitz-status-v3.pdf, algebra/carlitz-status-v3.tex, algebra/algebra.html, algebra/preliepbw.pdf, algebra/preliepbw.tex, algebra/dimcreation.pdf, algebra/dimcreation.tex, algebra/bilf.tex, algebra/bilf.pdf, algebra/r2t.pdf, algebra/r2t.tex, algebra/quaternion.tex, algebra/quaternion.pdf, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/skeletal.tex, algebra/skeletal.pdf, algebra/chromatic.tex, algebra/chromatic.pdf, algebra/dp-abstr-long.pdf, algebra/bcl.pdf, algebra/bcl.tex, algebra/cohom-errata.tex, algebra/leeuwen/alt-Schur-comments1.pdf, algebra/leeuwen/lrr-comments1.pdf, algebra/leeuwen/alt-Schur-comments1.tex, algebra/leeuwen/lrr-comments1.tex, algebra/leeuwen/foata-fest-comments1-updated.pdf, algebra/leeuwen/pictures-comments1.pdf, algebra/leeuwen/foata-fest-comments1-updated.tex, algebra/leeuwen/pictures-comments1.tex,

• Preprint Proof of a conjecture of Bergeron, Ceballos and Labbé, joint with Alexander Postnikov, added.
• Unfinished draft A note on non-broken-circuit sets and the chromatic polynomial added. (So far, it gives proofs of some generalizations of Whitney's theorem for the chromatic polynomial in terms of non-broken-circuit sets. It might eventually include a matroidal generalization as well.)
• Draft Do the symmetric functions have a function-field analogue? updated. Unfortunately, it is still far from complete, and proofs are given only for the most basic (and probably classical) facts.
• Preprint Double posets and the antipode of QSym updated. This is work in progress, and more will come soon.
• Expository note Why quaternion algebras have rank 4 added. (So far, 6 sections have been written, and a few more might be added some day.)
• New section: Work supervised. Apart from some links, it contains a note by Karthik Karnik and Anya Zhang on Chio Pivotal Condensation of determinants.
• PRIMES 2015 updated with new material.
• Note A note on bilinear forms added.
• More errata.
• Minor corrections and updates.

18 Dec 2015
files added/renewed: new.html, index.html, about.html, algebra/preliepbw.pdf, algebra/preliepbw.tex, algebra/dimcreation.pdf, algebra/dimcreation.tex, algebra/dimcreation-long.pdf, algebra/algebra.html, primes2015/sols.tex, primes2015/sols.pdf, primes2015/probs.pdf,

• Note On the PBW theorem for pre-Lie algebras finished.
• Note Dual immaculate creation operators updated.
• PRIMES 2015 updated with new material.
• Minor corrections and updates.

27 Nov 2015
files added/renewed: new.html, index.html, about.html, solutions.html, algebra/carlitz-status-v3.pdf, algebra/carlitz-status-v3.tex, algebra/derivat.pdf, algebra/derivat.tex, algebra/dimcreation.pdf, algebra/dimcreation.tex, algebra/topologies-errata.tex, algebra/topologies-errata.pdf, algebra/algebra.html, algebra/stanley-hyperplanes-errata-1b.tex, algebra/stanley-hyperplanes-errata-1b.pdf, algebra/polyhedral-cones.tex, algebra/polyhedral-cones.pdf, algebra/goldschmidt-errata.tex, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/preliepbw.pdf, algebra/preliepbw.tex, primes2015/sols.tex, primes2015/sols.pdf.

• Unfinished note On the PBW theorem for pre-Lie algebras added.
• Minor corrections and updates.
• More errata.

8 Nov 2015
files added/renewed: new.html, index.html, mrmoeb.pdf, mrmoeb.tex, frontiers.pdf, frontiers.tex, algebra/saliola-errata.pdf, algebra/saliola-errata.tex, algebra/r2t.pdf, algebra/r2t.tex, algebra/orzech.pdf, algebra/orzech.tex, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/groth1.pdf, algebra/groth1.tex, algebra/groth1alt.pdf, algebra/groth1alt.tex, primes2015/sols.tex, primes2015/sols.pdf, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/chicago2015.tex, algebra/chicago2015.pdf, algebra/algebra.html, algebra/va3.pdf, algebra/va3.tex, algebra/derivat.pdf, algebra/derivat.tex, about.html, about/cv.pdf, about/rs.pdf, about/ts.pdf, algebra/carlitz-status-v3.pdf, algebra/carlitz-status-v3.tex

• New draft Do the symmetric functions have a function-field analogue?.
• Preprint Pavel Galashin, Darij Grinberg and Gaku Liu, Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions updated.
• New note Collected trivialities on algebra derivations.
• About page (formerly the FAQ) revamped and updated, adding a CV and research and teaching statements.
• Various corrections to algebra notes (see file list above).

4 Oct 2015
files added/renewed: new.html, index.html, algebra/chicago2015.pdf, algebra/chicago2015.tex, algebra/algebra.html

• Added slides of a talk on dual stable Grothendieck polynomials.

28 Sep 2015
files added/renewed: new.html, index.html, algebra/dp-abstr.pdf, algebra/dp-abstr.tex, algebra/algebra.html

• New preprint: Double posets and the antipode of QSym.

14 Sep 2015
files added/renewed: new.html, index.html, solutions.html, algebra/orzech.pdf, algebra/orzech.tex, AMMA5715.pdf, AMMSRC.zip

• Added new solution: AMM problem A5715 (again, mostly written in 2009).
• Minor corrections in A constructive proof of Orzech's theorem.

13 Sep 2015 (2)
files added/renewed: new.html, index.html, solutions.html, frontiers.pdf, frontiers.tex

• Added new solution: At least |S|^k-1 · (|S| - 1) frontiers: a graph theory problem (mostly written in 2009).

13 Sep 2015
files added/renewed: new.html, index.html, primes2015/sols.tex, primes2015/sols.pdf, algebra/HopfComb.tex, algebra/HopfComb.pdf, algebra/HopfComb-sols.pdf, algebra/skeletal.tex, algebra/skeletal.pdf, geometry.html, geometry2.html, solutions.html, mrmoeb.pdf, mrmoeb.tex, MRSRC.zip, solutions.html, algebra/algebra.html, algebra/saliola-errata.tex, algebra/saliola-errata.pdf, algebra/groth1.tex, algebra/groth1.pdf, algebra/groth1alt.tex, algebra/groth1alt.pdf

• Added new preprint: Pavel Galashin, Darij Grinberg and Gaku Liu, Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions.
• Added Mathematical Reflections problem U275 with solution.
• Updates to various notes, in particular PRIMES 2015 and Hopf algebras in combinatorics.
• Added errata to Franco Saliola's "Hyperplane arrangements and descent algebras".

27 Jul 2015
files added/renewed: new.html, index.html, primes2015/sols.tex, primes2015/sols.pdf, hyperfactorialBRIEF.pdf, hyperfactorialLONG.pdf, hyperfactorialSRC.zip, algebra/HopfComb.tex, algebra/HopfComb.pdf, algebra/HopfComb-sols.pdf, algebra/skeletal.tex, algebra/skeletal.pdf, algebra/dimcreation.tex, algebra/dimcreation.pdf, algebra/dimcreation-long.pdf, algebra/skeletal-slides-mar2014.pdf, algebra/skeletal-slides-mar2014.tex, algebra/vienna2014.pdf, algebra/vienna2014.tex, algebra/r2t.tex, algebra/r2t.pdf

• New set of notes (works in progress): PRIMES 2015 reading project: problems and solutions.
• Updates to various notes, in particular to Hopf algebras in combinatorics.

8 Apr 2015
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/r2t.pdf, algebra/r2t.tex

• New draft preprint: The signed random-to-top operator on tensor space (draft).

12 Mar 2015
files added/renewed: new.html, index.html, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/HopfComb-sols.pdf, algebra/algebra.html, algebra/va3.pdf, algebra/va3.tex

• New scribe notes: Fundamentals of formal distributions (Lecture 3 of Vertex algebras by Victor Kac).
• Minor corrections to various algebra notes.

1 Feb 2015
files added/renewed: new.html, index.html, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/KP-errata-web.pdf, algebra/KP-errata-web.tex, algebra/algebra.html, algebra/orzech.pdf, algebra/orzech.tex, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/HopfComb-sols.pdf, algebra/skeletal-slides-mar2014.pdf, algebra/skeletal-slides-mar2014.tex, algebra/vienna2014.pdf, algebra/vienna2014.tex.

• Minor corrections to various algebra notes.

31 Jan 2015
files added/renewed: new.html, index.html, algebra/typos1web.pdf, algebra/typos1short.pdf, algebra/wittsrc.zip, algebra/algebra.html, algebra/orzech.pdf, algebra/orzech.tex, algebra/comes-ostrik-errata1.pdf, algebra/comes-ostrik-errata1.tex, algebra/higherlie-errata.pdf, algebra/higherlie-errata.tex.

• A constructive proof of Orzech's theorem added.
• Hopf algebras in combinatorics notes by Victor Reiner and me now contain a new chapter on Lyndon words and Hazewinkel's QSym generators, and are also available as an arXiv preprint. But the arXiv version is already lagging behind the version on the website.
• Updated old birational rowmotion slides and added new ones.
• Updated some other algebra notes, including Witt vector errata. Added two more sets of errata.

1 Oct 2014
files added/renewed: new.html, index.html, algebra/HopfComb.pdf, algebra/HopfComb.tex, algebra/HopfComb-sols.pdf, algebra/typos1web.pdf, algebra/typos1short.pdf, algebra/wittsrc.zip, algebra/witt5f.pdf, algebra/dimcreation.pdf, algebra/dimcreation.tex, algebra/algebra.html

• Dual immaculate creation operators draft added.
• Hopf algebras in combinatorics notes by Victor Reiner and me now contain a new chapter on Lyndon words and Hazewinkel's QSym generators, and are also available as an arXiv preprint.
• Updated old birational rowmotion slides and added new ones.
• Updated some other algebra notes, including Witt vector errata.

1 Aug 2014
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/skeletal-slides-mar2014.tex, algebra/skeletal-slides-mar2014.pdf, algebra/vienna2014.tex, algebra/vienna2014.pdf, FH1515.pdf, FH1515.tex, algebra/typos1web.pdf, algebra/typos1short.pdf, algebra/wittsrc.zip

• Hopf algebras in combinatorics notes by Victor Reiner and me updated with numerous new exercises. More to follow!
• Updated old birational rowmotion slides and added new ones.
• Updated some other algebra notes, including Witt vector errata.

5 June 2014
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/HopfComb.tex, algebra/HopfComb.pdf, algebra/HopfComb-sols.pdf,

• Hopf algebras in combinatorics notes by Victor Reiner and me are now available from this website (and updated again).

26 May 2014
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/pidisolift.tex, algebra/pidisolift.pdf, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/ipbrFPSAC6.pdf, algebra/ipbrFPSAC6.tex, faq.html, Dreigeom/index.html, modulussqrt.pdf, modulussqrt.tex, solutions.html,

• Added A modulus and square root inequality (see the solutions section).
• Updated Iterative properties of birational rowmotion, A note on lifting isomorphisms of modules over PIDs and FAQ. More serious updates to come...

1 April 2014
files added/renewed: new.html, index.html, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/ipbrFPSAC6.tex, algebra/ipbrFPSAC6.pdf, algebra/algebra.html, algebra/pidisolift.tex, algebra/pidisolift.pdf, algebra/algebra.html, algebra/skeletal-slides-mar2014.pdf, algebra/skeletal-slides-mar2014.tex,

• Updated Iterative properties of birational rowmotion.
  
• Some other changes.
  

22 December 2013
files added/renewed: new.html, index.html, algebra/skeletal.pdf, algebra/skeletal.tex, algebra/algebra.html,

• New paper (draft): Iterative properties of birational rowmotion I, with Tom Roby.
  

4 December 2013
files added/renewed: new.html, index.html, algebra/MO88399.pdf, algebra/MO88399.tex,

• Updated note: A representation-theoretical solution to MathOverflow question #88399. (Stupid errors removed, example and exercise added.)
  

21 November 2013
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/ipbrFPSAC6.pdf, algebra/ipbrFPSAC6.tex,

• Added The order of birational rowmotion (joint with Tom Roby), an extended abstract submitted for FPSAC 2014. The main paper is soon to follow.
• Added link to Boolean Witt vectors and an integral Edrei-Thoma theorem (joint with James Borger).

22 October 2013
files added/renewed: new.html, index.html, algebra/pbw.pdf, algebra/pbwlong.pdf, algebra/pbw.tex, algebra/pidisolift.pdf, algebra/pidisolift.tex, algebra/witt5.pdf, algebra/witt3.pdf, algebra/witt4.pdf, algebra/typos1short.pdf, algebra/typos1web.pdf, algebra/witt5f.pdf, algebra/algebra.html, perlen.pdf, Dreigeom/index.html, algebra/wittsrc.zip, algebra/rep2a.pdf, algebra/rep2.pdf, algebra/tensorext.pdf, algebra/tensorext.tex

• Poincaré-Birkhoff-Witt type results for inclusions of Lie algebras updated, fixing some typos and adding some references. In particular, the PBW-like statement for Clifford algebras has been located (with the same proof...) in Bourbaki's Algèbre IX *oops*... Also, I finally was shown how to get footnote numbering to work with the leftbar environment in LaTeX, so the footnotes now have (hopefully!) correct numbers.
• A few more updates to the Witt vectors sidenotes: Witt#5f has been added and a few older sidenotes have been corrected.
• Kleine Ergänzungen zu 1/n Summe von phi(d) q^n/d über alle d | n.

18 Apr 2013
files added/renewed: new.html, index.html, algebra/typos1short.pdf, algebra/typos1web.pdf, algebra/witt0.pdf, algebra/witt5e.pdf, algebra/witt5.pdf, algebra/witt5d.pdf, algebra/manchon-errata-update.pdf, algebra/manchon-errata-update.tex, algebra/witt5a.pdf, algebra/witt5c.pdf, algebra/witt5b.pdf, algebra/witt4.pdf, algebra/witt3.pdf, algebra/witt1.pdf, algebra/witt0.pdf, algebra/witt2.pdf, algebra/witt4a.pdf, algebra/witt4b.pdf, perlen.pdf, algebra/pidisolift.pdf, algebra/pidisolift.tex, algebra/algebra.html

• New note: A note on lifting isomorphisms of modules over PIDs.
• Notes taken in Pavel Etingof's 18.747 Infinite-dimensional Lie Algebras class at MIT cover Chapters 1 and 2, much of 3 and the basics of 4 now. They are still a far cry from completion and I hope to return to them (at least, to the non-Kac-Moody parts) in a while.
• Various updates to the Witt vectors sidenotes: added a couple more remarks to Hazewinkel's paper and fixed lots of mistakes of my own. More sidenotes will be added in foreseeable time. Also, Manchon errata corrected.
• 1/n Summe von phi(d) q^n/d über alle d | n an mehreren Stellen korrigiert. Leider werde ich wohl für längere Zeit nicht in der Lage sein, dieses Skript weiterzuführen.
• Hopfalgebren (in German) wieder aktualisiert (nichts bedeutendes, nur ein kleines Kuriosum mit Beweis).
  
• Minor corrections to Lambda-rings.

30 Oct 2012
files added/renewed: new.html, index.html, algebra/algebra.html, bilinear.pdf, MRSRC.zip, algebra/cohom-errata.pdf,

• Corrected some minor mistakes in A problem on bilinear maps (problem U228 in Mathematical Reflections).
• Another errata file added: Errata to William Crawley-Boevey: Cohomology and Central Simple Algebras.

6 Oct 2012
files added/renewed: new.html, index.html, geometry.html, geometry2.html, CircumRev.pdf, LD2005-5.pdf, LD2005-5.zip, JCG2012V1pp40-52.pdf, algebra/manchon-errata-update.pdf, algebra/manchon-errata-update.tex, algebra/sp-errata.pdf, algebra/sp-errata.tex, algebra/algebra.html

• Two more errata files added: Errata to Alexander E. Holroyd, Lionel Levine, Karola Mészáros, Yuval Peres, James Propp and David B. Wilson: Chip-Firing and Rotor-Routing on Directed Graphs, version v3 (2008) and Errata to Dominique Manchon: Hopf algebras, from basics to applications to renormalization, version v2 (2006).
• Added "new" geometry note Ehrmann's Third Lemoine Circle, recently published in Journal of Classical Geometry 1 (2012) pages 40-52.
• Corrected a mistake in Circumscribed quadrilaterals revisited found by George Baloglou, and also fixed the botched-up Fig. 11.

12 Aug 2012
files added/renewed: new.html, index.html, FH1515.pdf, FH1515.tex

• Aktualisiert: Fulton-Harris Proposition 15.15. Ironischerweise war in dieser Notiz, die einen Beweis in Fulton-Harris richtigstellen sollte, selbst ein Fehler enthalten (in Lemma 1 hatte ich es unterlassen, λ₁ + λ₂ + ... + λ_n = μ₁ + μ₂ + ... + μ_n zu fordern).

16 Jul 2012
files added/renewed: new.html, index.html, algebra/MO88399.pdf, algebra/MO88399.tex, bilinear.pdf, MRSRC.zip, algebra/algebra.html, solutions.html

• Updated note: A representation-theoretical solution to MathOverflow question #88399. (More details in the footnote, and fixed some parts of the proof being out of order.)
  
• New note: Solution to problem U228 in Mathematical Reflections. This contains three solutions, one of which was submitted with the problem.

10 Apr 2012
files added/renewed: new.html, index.html, 11409.pdf, AMMSRC.zip, MRSRC.zip, O219.pdf, maxperm.pdf, solutions.html

• Solutions to two Mathematical Reflections problems added (O219 and O222).

18 Feb 2012
files added/renewed: new.html, index.html, solutions.html, faq.html, algebra/algebra.html, algebra/MO88399.pdf, algebra/MO88399.tex, algebra/pbw.pdf, algebra/pbwlong.pdf, algebra/pbw.tex, algebra/tensorext.pdf, algebra/tensorext.tex, algebra/chevalley.pdf, algebra/chevalleys.pdf, algebra/chevalleySRC.zip, zeckendorfBRIEF.pdf, zeckendorfSRC.zip,

• Lambda-rings updated: now with with a completed Section 10 (Todd homomorphisms), examples (universal polynomials are now being explicitly computed for small values), a few new exercises, some proofs better detailed, and many mistakes corrected. And with a table of contents!
  
• Started taking lecture notes in Pavel Etingof's 18.747 Infinite-dimensional Lie Algebras class at MIT. Please note that only the first 20 or so pages are anywhere near finished right now!
• This site is now also hosted on the servers of the MIT.
  
• Added note: A representation-theoretical solution to MathOverflow question #88399.
  
• Updated note: Poincaré-Birkhoff-Witt type results for inclusions of Lie algebras (better numbering of theorems; less typos).
  
• Updated: Zeckendorf family identities generalized (also: long version).
• Added note: A few classical results on tensor, symmetric and exterior powers.
• Updated note: The Clifford algebra and the Chevalley map - a computational approach.

29 Aug 2011
files added/renewed: new.html, index.html, faq.html, algebra/algebra.html, algebra/kp-errata-web.pdf, algebra/witt2.pdf, algebra/witt3.pdf, algebra/witt5e.pdf, algebra/witt5d.pdf, algebra/witt5.pdf, algebra/friedlander-errata.pdf, 11451.pdf, 11452.pdf, 11453.pdf, AMM11453.pdf, AMMSRC.zip, solutions.html,

• Three more AMM solutions added

4 Jul 2011
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/pbw.tex, algebra/pbw.pdf, algebra/pbwlong.pdf, algebra/friedlander-errata.pdf,

• Poincaré-Birkhoff-Witt type results for inclusions of Lie algebras updated (more references, less typos).
  

17 Jun 2011
files added/renewed: new.html, index.html, faq.html, solutions.html, AMMSRC.zip, 11433.pdf, algebra/witt5a.pdf, algebra/witt4b.pdf, algebra/witt5.pdf, mo65420.tex, mo65420.pdf, algebra/algebra.html, algebra/pbw.tex, algebra/pbw.pdf, algebra/pbwlong.pdf, algebra/chevalley.pdf, algebra/chevalleys.pdf, algebra/chevalleySRC.zip, algebra/typos1short.pdf, algebra/typos1web.pdf, algebra/kp-errata-web.pdf,

• New note: Poincaré-Birkhoff-Witt type results for inclusions of Lie algebras. This text is being submitted for diploma thesis at the LMU Munich.
  
• A few Witt vectors sidenotes (see algebra) updated (typos corrected). Errata to Hazewinkel's Witt vectors extended.
  
• Updated The Clifford algebra and the Chevalley map - a computational approach with new results (and fixes).
  
• Hopfalgebren (in German) hat Version 0.1.89 erreicht.
• A few typos in lambda-rings corrected. More importantly, the text is now printable without breaking the borders.
  
• One more AMM solution added.
  
• mo65420 added.
  

5 Apr 2011
files added/renewed: new.html, index.html, algebra/chevalley.pdf, algebra/chevalleySRC.zip, solutions.html, AMM11424.pdf, 11424.pdf, 11458.pdf, AMMSRC.zip

• Updated The Clifford algebra and the Chevalley map - a computational approach. (Only detailed version updated: the typos were exclusive to it.)
• One more AMM solution added. Remark in the solution of #11458 corrected (it contained a wrong claim).
  

25 Mar 2011
files added/renewed: new.html, index.html, algebra/chevalley.pdf, algebra/chevalleys.pdf, algebra/witt4.pdf, algebra/witt4a.pdf, algebra/witt4b.pdf, algebra/witt5.pdf, algebra/witt5a.pdf, algebra/witt5b.pdf, algebra/witt5c.pdf, algebra/witt5d.pdf, algebra/witt5e.pdf

• Some algebra notes updated (concerns Witt vectors and Chevalley map).

23 Mar 2011
files added/renewed: new.html, index.html, solutions.html, algebra/rep2.pdf, zeckendorfBRIEF.pdf, zeckendorfLONG.pdf, zeckendorfSRC.zip, 11401.pdf, 11403.pdf, 11434.pdf, 11458.pdf, AMM11403.pdf, AMM11434.pdf, AMMSRC.zip, ComplexCos.pdf, ComplexCosSRC.zip, algebra/algebra.html, algebra/witt4.pdf, algebra/witt4a.pdf, algebra/goldschmidt-errata.pdf, algebra/chevalleySRC.zip, algebra/chevalleys.pdf, algebra/chevalley.pdf

• Three more AMM solutions uploaded.
• Updated (hopefully the last time): Zeckendorf family identities generalized (also: long version). Now with sourcecode. The brief version should also appear on arXiv in a few hours.
  
• Hopfalgebren (in German) updated (tensor coalgebra and shuffle coalgebra added as examples of coalgebras).
• New note: The Clifford algebra and the Chevalley map - a computational approach.
• Two problems on complex cosines now comes with sourcecode (and very minor update).
  

23 Feb 2011
files added/renewed: new.html, index.html, solutions.html, AMM11406.pdf, 11406.pdf, AMMSRC.zip

• One more solution to an AMM problem uploaded.

22 Feb 2011
files added/renewed: new.html, index.html, solutions.html, AMM11391.pdf, 11391.pdf, 11395.pdf, 11401.pdf, AMMSRC.zip, HallSRC.zip

• Another note now comes with TeX sourcecode.
  
• Three more solutions to AMM problems uploaded.

15 Feb 2011
files added/renewed: new.html, index.html, hyperfactorialSRC.zip, zeckendorfBRIEF.pdf, zeckendorfLONG.pdf, FH1515.pdf, FH1515.tex, VornicuSchurSRC.zip, Y1998SRC.zip, PopoviciuSRC.zip, subsetcondSRC.zip, solutions.html, 11435.pdf, 11407.pdf, AMM11407.pdf, MRSRC.zip, AMMSRC.zip, QEDMOSRC.zip, PFTBSRC.zip

• Some more notes now come with TeX sourcecode.
• Updated (typos fixed, again): Zeckendorf family identities generalized (also: long version).
• Fulton-Harris Proposition 15.15 hochgeladen (Teilskript von einem Vortrag).
• Hopfalgebren (in German) updated (III.4.20 is now complete, and more proofs added).
  
• More solutions to AMM problems uploaded.

4 Jan 2011
files added/renewed: new.html, index.html, algebra/rep2.pdf, perlen.pdf, Integrality.pdf, IntegralityBRIEF.pdf, IntegralitySRC.zip

• Hopfalgebren (in German) updated (now the coradical filtration is proven to be a coalgebra filtration).
• Updated A few facts on integrality: brief version is now brief indeed, and there is a sourcecode file.

20 Dec 2010
files added/renewed: new.html, index.html, faq.html, geometry.html, solutions.html, QEDMOEnglish.zip, MTProblem1.pdf, Dreigeom/index.html (was: Dreigeom/Inhalt.html), algebra/rep1.pdf, perlen.pdf, zeckendorfBRIEF.pdf, zeckendorfLONG.pdf, 11409.pdf, 11398.pdf, 11417.pdf, 11426.pdf, IntegralityBRIEF.pdf

• More solutions to AMM problems uploaded.
• Hopfalgebren (in German) updated (more proofs).
  
• Updated (typos fixed, again): Zeckendorf family identities generalized (also: long version), Math Time problem proposal #1 and 1/n Summe von phi(d) q^n/d über alle d | n.

1 Dec 2010
files added/renewed: new.html, index.html, Links.html, solutions.html, geometry.html, geometry2.html, Integrality.pdf, IntegralityBRIEF.pdf, perlen.pdf, zeckendorfBRIEF.pdf, zeckendorfLONG.pdf, Dreigeom/200402.zip

• The note A few facts on integrality now comes in a brief version and a detailed version. I don't think the latter will ever be needed... but it's there, since I wanted to formalize the proofs in order to make sure it is correct. Oh, and there is a part 5 now.
  Note: The introduction is to be slightly rewritten and parts 2-4 in the brief version are to be edited yet.
  
• Updated (only minor typo corrections): Zeckendorf family identities generalized (also: long version) and 1/n Summe von phi(d) q^n/d über alle d | n.
• Hopfalgebren (in German) updated (proof of Poincaré-Birkhoff-Witt made readable; a few more proofs added).
  
• Lösungen zu BWM 2004 Runde 2 neukompiliert: jetzt bessere Qualität bei kleineren Dateien.

26 Oct 2010
files added/renewed: new.html, index.html, hyperfactorialBRIEF.pdf, hyperfactorialLONG.pdf

• New note: A hyperfactorial divisibility (version 26 October 2010) (also: long version).

22 Oct 2010
files added/renewed: new.html, index.html, solutions.html, 11392.pdf, 11393.pdf, 11402.pdf, 11422.pdf, AMM11415.pdf, algebra/rep1.pdf, algebra/rep2.pdf, algebra/rep2a.pdf, zeckendorfBRIEF.pdf, zeckendorfLONG.pdf, perlen.pdf

• New note: Zeckendorf family identities generalized (version 21 October 2010) (also: long version).
• Updated pretty much everything in Advanced algebra (typo fixes mostly) and added a few new texts (albeit very boring).
• 1/n Summe von phi(d) q^n/d über alle d | n um neue Abschnitte erweitert (und noch lange nicht fertig).
• Solutions to some AMM problems uploaded. More are to come.

6 Apr 2010
files added/renewed: new.html, index.html, Dreigeom/Inhalt.html, algebra/algebra.html, algebra/rep1.pdf, algebra/rep2.pdf, algebra/rep2a.pdf, algebra/witt0.pdf, algebra/witt1.pdf, algebra/witt2.pdf, algebra/witt3.pdf, algebra/witt4.pdf, algebra/witt4a.pdf, algebra/witt4b.pdf, algebra/witt5.pdf, algebra/witt5a.pdf, algebra/witt5b.pdf, algebra/witt5c.pdf, algebra/witt5d.pdf, algebra/witt5e.pdf, perlen.pdf

• Updated pretty much everything in Advanced algebra (typo fixes mostly) and added a few new texts (albeit very boring).
• Neuer Artikel: 1/n Summe von phi(d) q^n/d über alle d | n (deutsche Version). Bislang nur Abschnitte 1-4 fertig. Irgendwann gibt es auch eine englische, aber zuerst muss die deutsche fertiggeschrieben werden.

25 Feb 2010 (update 2)
files added/renewed: new.html, index.html, algebra/algebra.html, algebra/witt5a.pdf

• One more note added to advanced algebra.

25 Feb 2010
files added/renewed: Dreigeom/QEDMO6P4deu.pdf, QEDMO7P8long.pdf, QEDMO7P8short.pdf, pen.txt, solutions.html, new.html, index.html, algebra/algebra.html, algebra/rep1.pdf, algebra/typos1short.pdf, algebra/typos1web.pdf, algebra/witt0.pdf, algebra/witt1.pdf, algebra/witt2.pdf, algebra/witt3.pdf, algebra/witt4.pdf, algebra/witt4a.pdf, algebra/witt4b.pdf, algebra/witt5.pdf

• New Advanced algebra section, along with some material to fill it. More will come.
• Solution to 7th QEDMO, Problem 8 (a slight extension of American Mathematical Monthly problem #E2353 by J. G. Rau) online.
• Ein paar Typos in Lösung der Aufgabe 4 der 6. QEDMO korrigiert.

9 Nov 2009
files added/renewed: Dreigeom/Inhalt.html, Dreigeom/Potenzger.pdf, geometry2.html, QEDMO4P13.pdf, solutions.html, new.html, index.html, faq.html

• This website is no longer avaliable from its old URL http://de.geocities.com/darij_grinberg/ . In fact, the webhoster (Yahoo Geocities) has discontinued its service. Now you can access my website through http://www.cip.ifi.lmu.de/~grinberg/ only. If this server fails, you can find an archived copy at http://sites.google.com/site/darijgrinberg/website (which, hopefully, won't fail too often).
  On the positive side, this means that the huge boldface notice about changing links is now of no use anymore, because if you can read it, you must already have the right URL ;)
• Added Solution to problem 13 of the 4th QEDMO. This is not really new content, because I have already posted this solution on MathLinks long ago, but I believe that the PDF is better written (or, rather, the MathLinks post was yet more unreadable than the PDF).
• Einige Eigenschaften der Potenzgeraden - das deutsche Original (ich habe die meisten Geometrietexte zuerst in Deutsch verfasst) von Radical axes revisited - ist jetzt online.
• FAQ updated. I think I know some more English now than I did 2 years ago when I wrote the FAQ...

24 Sep 2009
files added/renewed: QEDMO6P4long.pdf, Dreigeom/QEDMO6P4deu.pdf, Dreigeom/Inhalt.html, solutions.html, new.html, index.html

• Added links to Lambda-rings and Hopfalgebren (in German). Both of these projects are hosted on my Google page.
  Lambda-rings has now reached Version 0.0.3. I won't have too much time in the next month, but it will grow in future.
• Lösung der Aufgabe 4 der 6. QEDMO online.
• Added Solution to problem 4 of the 6th QEDMO.

7 Sep 2009
files added/renewed: Integrality.pdf, IntegralityOld.pdf, subsetcond.pdf, new.html, index.html

• A few facts on integrality and its old version updated to fix a mistake in Theorem 1, Assertion B.
• Proof of a CWMO problem generalized updated to include better references.

26 Aug 2009
files added/renewed: Dreigeom/UeberPara.pdf, Dreigeom/Brianchon.pdf, Dreigeom/AntiSteiner.pdf, Dreigeom/UmkreismittKreise.pdf, Dreigeom/KonkurrenteKreise.pdf, Dreigeom/Inhalt.html, new.html, index.html,

• Die deutsche Geometrieseite hat jetzt fünf "neue" Arbeiten. Diese Arbeiten sind eigentlich alt (2005 und früher), aber ich habe sie erst hochgestellt, nachdem ich einige von den Resultaten daraus in der 6. QEDMO als Aufgaben eingesetzt habe.

23 Aug 2009
files added/renewed: Integrality.pdf, IntegralityOld.pdf, new.html, index.html, Integrality2.pdf (removed)

• A few facts on integrality updated once again - part 4 this time.

20 Aug 2009
files added/renewed: Integrality2.pdf, solutions.html, Links.html, new.html, index.html

• A few facts on integrality, alternative version posted (a slight extension of Theorem 1, however forcing a rather obfuscated proof).
• A few mistakes on the webpage fixed.
• Some dead links in the link list fixed. 1 link added.

18 Aug 2009
files added/renewed: Integrality.pdf, new.html, index.html

• A few facts on integrality updated (parts 2 and 3 added; the note is now 26 pages long).

15 Aug 2009
files added/renewed: Popoviciu.pdf, PopoviciuFormal.pdf, RadicalAxis.pdf, MTProblem1.pdf, Yugoslavia1998.pdf, 19-9long.pdf, 19-9ML.pdf, geometry2.html, solutions.html, new.html, index.html

• Added some notes from 2007 that should have been published but were not (since the magazine never saw the light): Radical axes revisited, An inequality involving 2n numbers, Math Time problem proposal #1.
• Added Solution to Problem from the Book 19.9.
• Generalizations of Popoviciu's inequality (both versions) updated with references to a survey from 1993 that mentions most of the results. Apparently, if there is something new at all in my paper, then it's the proof (but even this needs not be so).

20 Jul 2009
files added/renewed: geometry.html, geometry2.html, Integrality.pdf, new.html, index.html

• Redesign of front page. Geometry papers and notes have their own subpages now.
• New note added: Darij Grinberg, A few facts on integrality (version 20 July 2009).
• WARNING: Soon, this site will not be avaliable from http://de.geocities.com/darij_grinberg/ anymore.
  (The webhoster, Yahoo Geocities, appears to be closing down. When they have closed, my website will only be avaliable at http://www.cip.ifi.lmu.de/~grinberg/, until I have found a new webhoster.

26 Apr 2009
files added/renewed: solutions.html, pene16.pdf, pen.txt, new.html, index.html

• New solution added: Project PEN, problem E16.

16 Apr 2009
files added/renewed: solutions.html, O111.pdf, O112.pdf, O114.pdf, U111.pdf, U112.pdf, new.html, index.html

• New section: Solutions to review problems, already filled with some content (albeit not very spectacular).

6 Apr 2009
files added/renewed: index.html, new.html, Popoviciu.pdf, PopoviciuFormal.pdf, pen.txt, faq.html, subsetcond.pdf

• New note: Proof of a CWMO problem generalized.
• Generalizations of Popoviciu's inequality (both versions) updated with a reference to Theorem 6.
• FAQ updated.
• New problem published: Darij Grinberg, Cezar Lupu, Problem 896, College Mathematics Journal, 2009 no. 2 (March 2009).

18 Nov 2008
files added/renewed: index.html, new.html, pen.txt

• This site will soon disappear from http://www.stud.uni-muenchen.de/~darij.grinberg/ !
  Please change your links to http://www.cip.ifi.lmu.de/~grinberg/ .
  (The LMU is discontinuing to offer webspace for students on their servers. Fortunately, the Informatics Institute has its own hosting.)

20 Oct 2008
files added/renewed: index.html, new.html, Links.html, errata.html

• Updated the errata page with one more from Altshiller-Court.
• Link list slightly updated.

11 Oct 2008
files added/renewed: index.html, new.html, links.html, Dreigeom/Inhalt.html, Dreigeom/HBeckerBWM20062.zip

• Hanno Beckers Lösungen der 2. Runde des Bundeswettbewerbs Mathematik 2006 sind endlich lesbar - der Fehler lag auf meiner Seite.

13 Sep 2008 (ii)
files added/renewed: index.html, new.html, links.html, errata.html, errata1.html

• Updated the errata page.
• Link list updated due to the takedown of the Kalva site (check it out using the Wayback Machine). Whoever is responsible for the site going offline has earned a boo from the whole community...

13 Sep 2008 (i)
files added/renewed: index.html, new.html, CircumRev.pdf

• The note Circumscribed quadrilaterals revisited has been updated once again to include another theorem from MathLinks with a (new?) proof.

10 Sep 2008
files added/renewed: index.html, new.html, CircumRev.pdf

• The note Circumscribed quadrilaterals revisited has been updated to include some new material.
  To be honest, the new results are rather obvious; a more serious update may come soon.

23 Jul 2008
files added/renewed: index.html, new.html, pen.txt, NMMathesis.zip, Links.html

• Thanks to the help of Francisco Bellot Rosado, I have obtained the Mathésis article by V. Thébault and A. Mineur referenced as [6] in my article on The Neuberg-Mineur circle.
• PEN posts updated (inserted some new links).
• The link list was updated.

25 Mar 2008
files added/renewed: index.html, new.html, faq.html, errata.html, Popoviciu.pdf, PopoviciuFormal.pdf, pen.txt

• Generalizations of Popoviciu's inequality updated (corrected a linguistic mistake: in the formulations of Theorems 13 and 14, the word "assertion" could be misunderstood; now I have replaced it by "condition").
• PEN posts updated (inserted some new links).
• The errata page now also features Honsberger's book.

20 Mar 2008
files added/renewed: index.html, new.html, Popoviciu.pdf, PopoviciuFormal.pdf

• Generalizations of Popoviciu's inequality published on arXiv and added to this website.

14 Mar 2008
files added/renewed: index.html, new.html, StPeters2003.pdf

• Note edited: St. Petersburg 2003: An alternating sum of zero-sum subset numbers (put Lemmata 1-3 into the beginning; now it should be much less confusing).

13 Mar 2008
files added/renewed: index.html, new.html, faq.html, StPeters2003.pdf

• Note extended: St. Petersburg 2003: An alternating sum of zero-sum subset numbers (slightly restructured and Problem 2 added).
• FAQ updated.

15 Feb 2008
files added/renewed: index.html, new.html, faq.html, errata.html, StPeters2003.pdf

• Note added: St. Petersburg 2003: An alternating sum of zero-sum subset numbers.
• FAQ updated and an experimental page for errata in books created.

17 Dec 2007
files added/renewed: index.html, new.html, faq.html, O49.pdf

• New problem added: Cosmin Pohoata and Darij Grinberg, Problem F07-1, The Harvard College Mathematics Review, Vol. 1, No. 2, Fall 2007.
• FAQ updated: The public domain dedication contained some mistakes (both of spelling and of content).
• Proposed solution to Mathematical Reflections problem O49 added.

28 Nov 2007
files added/renewed: index.html, new.html, S64.pdf

• Proposed solution to problem S64 from Mathematical Reflections added.

31 Oct 2007
files added/renewed: index.html, new.html, QEDMOEnglish.zip

• The statements of the QEDMO problems in English updated: added problems of the 5th QEDMO.

6 Oct 2007
files added/renewed: index.html, new.html, Hall.pdf, HallAbridged.pdf

• Fixed two typos in An algebraic approach to Hall's matching theorem and in the abridged version of the same article.

5 Oct 2007
files added/renewed: index.html, new.html, Dreigeom/Inhalt.html, Dreigeom/Feuerbach.pdf, Dreigeom/Feuerbach.zip (removed), NewNinepoint/winkel.jpg, NewNinepoint/Feuer1.gif, NewNinepoint/Feuerbach.html

• Some more published problems added to the index.
• Edited the old note "New Insight on the Ninepoint Circle", fixing a mistake in the proof of Theorem 1. It is an outdated note anyway.
• Habe die Arbeit "Karl Wilhelm Feuerbach, sein Kreis und die Dreiecksgeometrie" erneuert. Alles, was ich dabei geändert habe, ist der Beweis von Satz 1, wo ich einen dummen Fehler verbessert habe. Bitte nicht wundern, daß die Arbeit eine Seite kürzer (habe den Rand verkleinert) und die PDF-Datei signifikant kleiner (habe sie mit einer neueren Ghostview-Version kompiliert) geworden ist.
• Liste der Veröffentlichungen in der WURZEL um ein paar Aufgaben ergänzt (alle die bis jetzt erschienen sind).

3 Oct 2007
files added/renewed: index.html, new.html, Links.html, Hall.pdf, HallAbridged.pdf, Dreigeom/HBeckerBWM20062.zip (removed), Dreigeom/SchlEG.pdf, Dreigeom/Inhalt.html

• Note added: An algebraic approach to Hall's matching theorem, with its abridged version.
• Habe meine alte Facharbeit "Schließungssätze in der ebenen Geometrie" auf Wunsch einiger Personen hin online gestellt.
• Hanno Beckers Lösungen zur 2. Runde vom BWM 2006 sind jetzt gelöscht, weil die ZIP-Datei defekt war (und der Autor seine Originalversion verloren hat).
• The link list was updated with a new German link.

26 Aug 2007
files added/renewed: index.html, new.html, O25.pdf, faq.html

• Proposed solution to Mathematical Reflections problem O25 is now online (but shouldn't be of any interest).

13 Aug 2007
files added/renewed: index.html, new.html, VornicuS.pdf, pen.txt, faq.html, QEDMOEnglish.zip

• New note: The Vornicu-Schur inequality and its variations. Not so new actually, but now it's open to everyone. :)
• PEN posts updated.
• The statements of the QEDMO problems in English edited (2nd and 4th QEDMO).
• FAQ updated with a reference to Nathan Altshiller-Court, College Geometry and reviews of two inequalities books.

9 Jul 2007
files added/renewed: index.html, new.html, faq.html, QEDMOEnglish.zip

• Now the archive with the the statements of the QEDMO problems in English contains all four QEDMO's organized so far.
• Added link to Problem O49.

28 Jun 2007
ALSO see 19 Jun 2007, 30 May 2007 and 9 Mar 2007 for server (3)
files added/renewed: index.html, new.html, faq.html, Dreigeom/Inhalt.html, DreiGeom/QEDMO4g.zip

• Die Lösungsbeispiele zu den Geometrieaufgaben der 4. QED-Mathematik-Olympiade sind da.
• Additions to FAQ.
• Finally the server (3) seems to work properly again.

19 Jun 2007
ALSO see 30 May 2007 and 9 Mar 2007 for server (3)
files added/renewed: index.html, new.html, GergonneEuler.pdf, me.html (removed), faq.html, pen.txt, QEDMOEnglish.zip

• Added note An unexpected application of the Gergonne-Euler theorem.
• Added a FAQ (and a few files related to it). I hope it is of help.

30 May 2007
ALSO see 9 Mar 2007 for servers (2) and (3)
files added/renewed: index.html, new.html, TPSymmedian.pdf, DreiGeom/Inhalt.html, NeubergMineur.pdf, DreiGeom/NeubergMineurDeutsch.pdf

• Added note The Neuberg-Mineur circle as well as its German version Der Neuberg-Mineurkreis.
• An article and a problem added to the list of publications.
• Minimal changes in Three properties of the symmedian point (fixed a typo).

9 Mar 2007
files added/renewed: index.html, new.html, DreiGeom/Inhalt.html, Dreigeom/QEDMO4a.zip

• Die Lösungsbeispiele zu den zwei Algebraaufgaben der 4. QED-Mathematik-Olympiade sind da - erstmal nur auf dem Geocities-Server. Geometrie wird in absehbarer Zukunft folgen.

16 Feb 2007
files added/renewed: index.html, new.html, BalticFeuer.zip, Butterfly.zip, ButterflyS.html
ALSO see 3 Feb 2007 for servers (2) and (3)

• New note: On cyclic quadrilaterals and the butterfly theorem.
• Added a copy of the paper From Baltic Way to Feuerbach - A Geometrical Excursion, published in Mathematical Reflections 2/2006 pages 1-20, to this site with some graphical errors fixed.
• Design of index page (hopefully) improved, along with the descriptions/abstracts of some notes.

3 Feb 2007
files added/renewed: index.html, new.html, links.html, NewNinepoint/Feuerbach.html, YiuSynth.zip, YiuSynthPDF.zip, YiuSynth/ (directory removed), SymmedianPedal.zip, SymmedianPedalPDF.zip, SymmedianPedal/ (directory removed), ComplexCos.pdf

• New note: Two problems on complex cosines.
• The link list now contains a whole section of links to internet libraries.
• the URLs should now be changed).

29 Dec 2006
files added/renewed: index.html, new.html, links.html, me.html, CircumRev.pdf, Dreigeom\Inhalt.html, Schroeder\Schroeder.html

• Circumscribed quadrilaterals revisited has been unsubstantially edited (references to MathLinks topics have changed because of merging topics).
• Shortcuts added to index.html. Hope they are of help. Some minor updates to the rest of the site (in most cases, descriptions for various stuff were made more understandable).

23 Sep 2006
files added/renewed: index.html, new.html, Isogonal.zip, Isogonal.zip

• Isogonal conjugation with respect to a triangle has now been extended. Because of problems with compilation, I had to put some of the graphics in an extra file, so the whole is in a ZIP archive now.

9 Sep 2006
files added/renewed: index.html, new.html, Dreigeom\Inhalt.html, Dreigeom\HBeckerBWM20062.zip, Dreigeom\DHarrerBWM_Runde2_2006.zip

• Hanno Beckers und Daniel Harrers Lösungen der 2. Runde des Bundeswettbewerbs Mathematik 2006 sind hoch.

8 Sep 2006
files added/renewed: index.html, new.html, Isogonal.zip, Dreigeom\Inhalt.html, Dreigeom\200602.zip

• Added a reference to Isogonal conjugation with respect to a triangle.
• Die Lösungen der 2. Runde des Bundeswettbewerbs Mathematik 2006 sind da. (Und ich kann euch versichern, ihr wollt sie nicht sehen. Har har har.)

3 Sep 2006
files added/renewed: index.html, new.html, Dreigeom\QEDMO3g.pdf

• Die Lösungsbeispiele zu den Geometrieaufgaben der 3. QED-Mathematik-Olympiade wurden um einen Satz 3 c) bei Aufgabe G2 ergänzt. Die inkorrekt dargestellten Zeichnungen zu Aufgabe G2 wurden aus der Lösungs-PDF entfernt (jetzt sind sie nur noch in der zweiten PDF zu finden).

1 Sep 2006
files added/renewed: index.html, new.html, Isogonal.zip, Dreigeom\Inhalt.html, Dreigeom\QEDMO3g.pdf

• Die Lösungsbeispiele zu den Geometrieaufgaben der 3. QED-Mathematik-Olympiade sind da.
• Fixed minor bugs in Isogonal conjugation with respect to a triangle (for some mystical reason, the segment PQ disappeared each time Fig. 13 was compiled - making the segment dashed stopped this strange behaviour; also, corrected a misspelling of my name in the list of references :) ).

28 Aug 2006

• Lösungsbeispiele zu den Algebraaufgaben der 3. QED-Mathematik-Olympiade leicht ergänzt (dritter Beweis von (A1.1) bei Aufgabe A1 hinzugefügt). Die Geometrieaufgaben werden in absehbarer Zeit folgen.
• Die Lösungen der 2. Runde des Bundeswettbewerbs Mathematik 2006 sind fertig und werden 1 Woche nach Einsendeschluss (1. September 2006) hochgestellt. Dies wird auch die letzte Runde des BWM sein, an der ich teilnehme.
• Minor updates throughout the site, mostly in the links section.

• Change of official email address! [19 Jan 2006]
  My new email address is
  AB=gmail.com
  where the letter A should be replaced by darij
  the letter B should be replaced by grinberg
  and the sign = by the sign @.
  The old address (which ends with web.de) is dead. Please don't send mails to there anymore.

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Darij Grinberg