Errata and marginalia

• Errata to Arvind Ayyer, Steven Klee, Anne Schilling: Combinatorial Markov chains on linear extensions, arXiv:1205.7074v3.
  LaTeX sourcecode of the errata.
  There wasn't much to correct here, but on the last page I state a new conjecture.
  
  
• Errata to John A. Beachy, William D. Blair: Abstract Algebra, 4th edition 2019.
  LaTeX sourcecode of the errata.
  A friendly undergraduate-level textbook with a plenitude of exercises, many of them solved. The errata also cover the auxiliary materials on John Beachy's website.
  
  
• Errata to D. Blessenohl and H. Laue: Algebraic combinatorics related to the free Lie algebra.
  LaTeX sourcecode of the errata.
  There are very few (and very minor) mistakes in the paper that I'm aware of, but the writing is quite terse and abstract. I add details omitted from the proof of Solomon's Mackey formula (Proposition 4.3). Note that this proof is self-contained and does not rely on the rest of the paper (fortunately, as it is the most readable part).
  
  
• Errata to Murray R. Bremner, Sara Madariaga, Luiz A. Peresi: Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions.
  LaTeX sourcecode of the errata.
  Chapter 1 of this paper gives a beautiful and quick survey (with proofs) of the classical approach to the (characteristic-0) representations of the symmetric group via the Young natural basis. I correct some (very few) minor inaccuracies and add details to various proofs.
  
  
• Errata to Emmanuel Briand: When is the Algebra of Multisymmetric Polynomials Generated by the Elementary Multisymmetric Polynomials?.
  LaTeX sourcecode of the errata.
  The main erratum to this nice paper is the wrong proof of Lemma 13.
  
  
• Errata to Kenneth S. Brown: Semigroups, rings, and Markov chains, arXiv:math/0006145v1.
  LaTeX sourcecode of the errata.
  This corrects errors and adds some details.
  
  
• Errata to Kenneth S. Brown: Semigroup and Ring Theoretical Methods in Probability.
  LaTeX sourcecode of the errata.
  This corrects a few trivial errors.
  
  
• Errata to Peter J. Cameron: Combinatorics 1: The art of counting (vol. 1 of St Andrews Notes on Advanced Combinatorics).
  LaTeX sourcecode of the errata.
  Errata covering most chapters of a set of lecture notes on combinatorics. Include a few alternative proofs.
  
  
• Errata to Damien Calaque, Kurusch Ebrahimi-Fard, and Dominique Manchon: Two interacting Hopf algebras of trees (arXiv:0806.2238v4).
  LaTeX sourcecode of the errata.
  This paper first observed an interaction between two combinatorial Hopf algebras on trees -- one defined in terms of admissible cuts (lower/upper order ideal decompositions) and one defined in terms of edge contractions. (And did many other things, many of which I have not read...)
  
  
• Errata to Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello: Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities, arXiv:0809.3516v2.
  LaTeX sourcecode of the errata.
  A highly recommended paper that gives modern but elementary proofs to the Capelli and Cayley identities (and more). In the errata, I correct minor errors, fill a gap in one of the proofs, and answer a question posed at the end of the paper (viz., how to derive the all-minors Cayley identity using the tools in the paper).
  
  
• Errata to Pierre Cartier: A primer of Hopf algebras.
  LaTeX sourcecode of the errata.
  Corrections to some parts of the primer (I have not read it in full).
  
  
• Errata to Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli: Representation Theory of the Symmetric Groups, 2010.
  A text on symmetric group representations. My interest was mostly focused on Chapters 3 and 6, so the errata are likely far from complete (but this is a crowdsourced list, so it may grow without my help). The Okounkov--Vershik approach itself is rather finicky and marred by several gaps and mistakes in this and several other sources; to my knowledge, the best treatment of it is Martin Lorenz, A Tour of Representation Theory, though I have not read much of it.
  
  
• Errata to Jonathan Comes, Victor Ostrik: On blocks of Deligne's category Rep(S_t), version v2 (2010).
  LaTeX sourcecode of the errata.
  These are essentially sidenotes I made back in 2013 when I was reading the Comes-Ostrik paper. Minor gaps are filled in the proofs of Lemmas 3.1 and 5.4, and the statements of Proposition 4.3 and Theorem 4.8 are corrected. (Other than this, mostly typos.)
  
  
• Errata to William Crawley-Boevey: Cohomology and Central Simple Algebras.
  LaTeX sourcecode of the errata.
  There was not much to correct here, but here it is for the sake of completeness.
  
  
• Errata to Michael W. Davis: The Geometry and Topology of Coxeter Groups.
  LaTeX sourcecode of the errata.
  Chapters 3--4 in this book offer a brief but substantial combinatorial treatment of Coxeter groups. The errata fill in some missing details in proofs and correct some errors (the only major mistake fixed here is a missing condition in the definition of pre-reflection systems).
  
  
• Errata to Willem de Graaf: Computational Algebra (version 2022).
  LaTeX sourcecode of the errata.
  This is my second list of corrections; the first one have already been corrected in 2021.
  
  
• Errata to Tom Denton, Florent Hivert, Anne Schilling and Nicolas M. Thiéry: On the representation theory of finite J-trivial monoids (arXiv:1010.3455v3).
  LaTeX sourcecode of the errata.
  I started reading the paper, but got distracted by basic properties of Green classes. So here are (mostly) proofs of these basic properties :)
  
  
• Translation (with corrections) of Jacques Désarménien: Modulo-n study of Mahonian statistics (Étude modulo n des statistiques mahoniennes), Séminaire Lotharingien de Combinatoire, B22a (1989).
  LaTeX sourcecode of the translation.
  This paper (originally in French) obtains various enumerative results from the study of polynomials "even modulo a positive integer n". These are polynomials having the property that the coefficient of a^k depends only on the greatest common divisor of k and n.
  This translation is also available on the website of the journal.
  
  
• Unofficial re-edition of J. Désarménien, Joseph P. S. Kung, Gian-Carlo Rota: Invariant Theory, Young Bitableaux, and Combinatorics, Advances in Mathematics, Volume 27, Issue 1, January 1978, pp. 63--92, doi:10.1016/0001-8708(78)90077-4.
  LaTeX sourcecode of the re-edition.
  A classical paper proving the straightening "formula" for the letterplace algebra (i.e., the coordinate ring of the matrix space K^{n × k} over a field K) and the First and Second Fundamental Theorems for the invariants (in an appropriate sense) of GL_d(K) on K^{n × d} (that is, GL_d(K) acting on n vectors in K^d). The proofs are characteristic-free and partly combinatorial. The re-edition corrects various errors as well as adding details to the proofs.
  
  
• Errata to Peter G. Doyle: Frobenius's last proof, arXiv:1904.06573v1.
  LaTeX sourcecode of the errata.
  This is a neat exposition of an elementary proof of the Rogers-Ramanujan identities (via a finitary version).
  
  
• Errata to Jan Draisma and Dion Gijswijt: Invariant Theory with Applications.
  LaTeX sourcecode of the errata.
  This is a nice set of notes with several interesting features, such as an elementary proof of Schur-Weyl duality in Section 11.1. I have not read it in full, but the errata cover a significant part of the text.
  
  
• Unofficial re-edition of A. W. M. Dress and W. Wenzel: A Simple Proof of an Identity Concerning Pfaffians of Skew Symmetric Matrices, Advances in Mathematics 112 (1995), pp. 120--134, doi:10.1006/aima.1995.1029.
  LaTeX sourcecode of the re-edition.
  This paper presents a new and slick approach to Pfaffians via a recursively-defined linear endomorphism of the exterior algebra. As applications, the authors reprove the classical Pf² = det identity as well as a Plücker-like identity.
  
  
• Errata to Kurusch Ebrahimi-Fard, Frédéric Patras: From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras, arXiv:1911.08766v1.
  LaTeX sourcecode of the errata.
  This is a friendly introduction to Rota-Baxter algebras and their connections to various structures in algebra, combinatorics and analysis. I add some details and correct some typos.
  
  
• Errata to Eric S. Egge: An Introduction to Symmetric Functions and Their Combinatorics.
  LaTeX sourcecode of the errata.
  This is an elementary, undergraduate-friendly combinatorial introduction to the theory of symmetric functions. I have read most of it (and reviewed it for ZBMath). Eric Egge keeps his own lists of corrections and commentary on his website, which probably includes mine (but is less detailed?).
  
  
• Errata to Noam D. Elkies: On finite sequences satisfying linear recursions, arXiv:math/0105007v2.
  LaTeX sourcecode of the errata.
  This is not the first paper to prove the classical result that a Hankel matrix of size n × n with entries randomly chosen from a finite field F (uniformly and independently) has probability 1/|F| to be singular. However, it probably gives the most conceptual proof, relating the result to ideals and actions of the polynomial ring.
  
  
• Errata to Pavel Etingof and Xiaoguang Ma: Lecture Notes on Cherednik Algebras, arXiv:1001.0432v4.
  LaTeX sourcecode of the errata.
  The errata cover only the first 10 pages. They are not as much errata as extra details I had to fill in when reading this (extremely terse) set of notes. (Alas, the notes went over my head around page 10...) The "errata" include an alternative proof of Proposition 2.18 which uses no transcendental methods (but takes nearly 20 pages of computation).
  
  
• Errata to Valentin Féray: Approche Duale des représentations du groupe symétrique, 2016.
  LaTeX sourcecode of the errata.
  Corrections to algebraic/combinatorial parts of these nice notes.
  
  
• Errata to P. Fleischmann: A New Degree Bound for Vector Invariants of Symmetric Groups, Trans. Amer. Math. Soc. 350 (1998), pp. 1703--1712.
  LaTeX sourcecode of the errata.
  Minor corrections to a nice and useful article.
  
  
• Errata to Loic Foissy and Claudia Malvenuto: The Hopf algebra of finite topologies and T-partitions, arXiv:1407.0476v2.
  LaTeX sourcecode of the errata.
  This is a really nice preprint, which has now been published (Journal of Algebra, Volume 438, 15 September 2015, Pages 130--169); unfortunately, many of the errors are still extant in the published version.
  Speaking of this, here is a draft of a note in which I tried to apply the Foissy-Malvenuto Hopf algebra to prove a formula of Menous, Novelli and Thibon relating combinatorial Hopf algebras to polyhedral cones. My proof ended up irritatingly long and technical, but maybe the intermediate results are of some use. (Sourcecode.)
  
  
• Errata to Sergey Fomin and Curtis Greene: Noncommutative Schur functions and their applications, Discrete Mathematics 306 (2006), pp. 1080–1096.
  LaTeX sourcecode of the errata.
  This paper is already a classic; it generalizes the (skew) Schur functions to a "mildly" noncommutative setting in which they still commute even though the variables don't. I have not found much to correct, but I ended up adding lots of details to some terse proofs, particularly filling in the proof of Lemma 3.3.
  
  
• Errata to Robin Forman: Discrete Morse theory and the cohomology ring.
  LaTeX sourcecode of the errata.
  The first two sections of this paper form a nice introduction to discrete Morse theory (specifically, its homological consequences); I have filled in some omitted proofs and corrected a few typos.
  
  
• Errata to Robin Forman: Combinatorial Novikov-Morse theory.
  LaTeX sourcecode of the errata.
  Minor corrections to another discrete Morse theory paper I have only selectively skimmed.
  
  
• Errata to F. G. Friedlander, M. Joshi: Introduction to the theory of distributions, 2nd edition, Cambridge University Press 1998.
  This is a list of mistakes I caught in the first chapters (mostly 1-5 and 7) of the text. The majority of these are typographical; only a few seem to actually be of mathematical nature.
  Note: Apparently I am not the only person keeping a list of errata in this book. (My list neither contains, nor is contained in, Koornwinder's.)
  
  
• Errata to William Fulton: Young tableaux, 1999.
  One of the best texts on Young tableaux -- both the combinatorics and the related representation theory (I am not familiar with the geometry part). The list is crowdsourced -- your additions are welcome!
  
  
• Darij Grinberg, Fulton-Harris Proposition 15.15 (in German) (Version 29. Januar 2011).
  PDF-Datei; siehe auch TeX-Quellcode.
  
  Ein Beweis, dass die Darstellung von GL(V), die man durch Schur-Weyl-Dualität aus der irreduziblen Darstellung c_λℂ[S_m] von S_m erhält, als Darstellung der Liealgebra sl(V) das höchste Gewicht λ₁L₁ + λ₂L₂ + ... + λ_nL_n hat (wenn die Cartan-Unteralgebra und die Weylkammer "richtig" gewählt wird). Dies ist Proposition 15.15 in Fulton-Harris, wo ein nicht ganz richtiger Beweis gegeben wird. Der Beweis hier versucht, diesen Fehler zu vermeiden.
  
  See also: Crowdsourced list of errata for Fulton/Harris on MathOverflow.
  
  
• Errata to Vesselin Gasharov: A short proof of the Littlewood-Richardson rule, 27 August 1998.
  LaTeX sourcecode of the errata.
  Corrections to a classical paper in symmetric functions theory (a precursor to Stembridge's even shorter proof, which I also highly recommend).
  
  
• Errata to I. Gessel, A. Restivo, and C. Reutenauer: A bijection between words and multisets of necklaces, European Journal of Combinatorics 33, Issue 7, October 2012, pp. 1537--1546.
  This corrects the proof of the bijectivity of the Gessel-Reutenauer bijection Φ.
  
  
• Errata to Ira M. Gessel and Christophe Reutenauer: Counting permutations with given cycle structure and descent set, Journal of Combinatorial Theory, Series A 64, Issue 2, November 1993, pp. 189--215.
  This corrects the proof of the well-definedness of the Gessel-Reutenauer bijection U.
  
  
• Errata to Ira M. Gessel and X. V. Viennot: Determinants, Paths, and Plane Partitions, version of 28 August 2000.
  LaTeX sourcecode of the errata.
  This corrects some typos and adds more details to a classical preprint. (I have read only the parts that related to the Jacobi-Trudi identities.)
  
  
• Unofficial re-edition of A. Giambruno and S. K. Sehgal: On a Polynomial Identity for n × n Matrices, Journal of Algebra 126 (1989), pp. 451--453, doi:10.1016/0021-8693(89)90312-8.
  LaTeX sourcecode of the re-edition.
  This proves an identity for 4n arbitrary n×n-matrices over a commutative ring -- a kind of twin to the Amitsur--Levitzki identity.
  
  
• Errata to S. Gill Williamson: The common-submatrix Laplace expansion.
  LaTeX sourcecode of the errata.
  Errata for a nice elementary proof of the "common-submatrix Laplace expansion" (a powerful determinantal identity).
  
  
• Errata to David M. Goldschmidt: Group Characters, Symmetric Functions, and the Hecke Algebra.
  LaTeX sourcecode of the errata.
  These might not be complete, as I have not read the third part of the book. (I recommend Part II.)
  
  
• Errata to Frederick M. Goodman: Algebra: Abstract and Concrete.
  LaTeX sourcecode of the errata.
  Some corrections to a pedagogically valuable but somewhat rough-at-the-edges (and rather terse) text on abstract algebra.
  
  
• Errata to J. A. Green: Polynomial Representations of GL_n, 2nd edition 2007.
  LaTeX sourcecode of the errata.
  These errata concern the (freely available) Appendix on Schensted correspondence and Littelmann paths by K. Erdmann, J.A. Green and M. Schocker, which gives detailed and rigorous proofs of several classical properties of Robinson-Schensted insertion and coplactic operations on words and Young tableaux. The errata correct various minor lapses and incongruities, thus hopefully rendering the appendix as smoothly readable as it should be. A simplified proof of the Littlewood--Richardson rule (using the same combinatorial tools but avoiding the representation theory) is also given.
  
  
• Errata to Tom Halverson, Arun Ram: Partition Algebras, arXiv:math/0401314v2.
  LaTeX sourcecode of the errata.
  I've read (and learnt a lot from) parts of this paper. It is instructive, although somewhat chaotically written (it appears that the sections are supposed to be read starting with Section 5).
  
  
• Errata and sidenotes to Michiel Hazewinkel: Witt vectors. Part 1.
  This is a long and eclectic expository paper that I have read as an undergraduate around 2010; it was here that I encountered the charm of symmetric functions for the first time. Besides a long list of typos, I have written a few notes on the subject (warning: undergraduate work, not very polished).
  
  
• Errata to Michiel Hazewinkel, Nadiya Gubareni, V. V. Kirichenko: Algebras, Rings and Modules: Lie Algebras and Hopf Algebras.
  LaTeX sourcecode of the errata.
  This is a somewhat haphazard collection of errors I found in this book (which is well-written, educational and enjoyable, if lacking in proofreading); most importantly, it documents a gap in the proof of Theorem 6.5.8 (which I don't know how to fix).
  
  
• Unofficial re-edition of P. J. Higgins: Baer Invariants and the Birkhoff-Witt Theorem, Journal of Algebra 11 (1969), pp. 469--482, doi:10.1016/0021-8693(69)90086-6.
  LaTeX sourcecode of the re-edition.
  This classical paper relaxes the assumptions of the Poincaré-Birkhoff-Witt theorem from "Lie algebras over a field" to "Lie algebras on any sufficiently nice ground module". Here, niceness is defined in terms of a homological invariant (one of the Baer invariants); in particular, any flat modules are included, as are any modules over a Q-algebra.
  The re-edition includes an alternative proof of a key lemma, and an application to flat modules that was left unstated in the original paper.
  
  
• 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).
  LaTeX sourcecode of the errata.
  There are only few real mistakes here (and they can be easily fixed, maybe with the exception of the one in the proof of Lemma 2.8). Most of this file are clarifications for some arguments which I found nontrivial to follow.
  The Holroyd-Levine-Mészáros-Peres-Propp-Wilson article is an exposition of one of the most striking (in my opinion) modern developments in combinatorics.
  Warning: The authors have updated the arXiv version of the paper (thank you!), correcting most of the errors in my list of errata (but not the proof of Lemma 2.8, unfortunately). Thus my errata are almost completely obsolete.
  
  
• Errata to Roger Howe and Soo Teck Lee: Why should the Littlewood–Richardson rule be true?, Bull. Amer. Math. Soc. 49 (2012), pp. 187--236.
  LaTeX sourcecode of the errata.
  This article (which I have never read in full) proves the Littlewood-Richardson rule on about 40 pages, and the proof is far from self-contained (it relies on standard monomial theory and some invariant theory). Personally, I don't believe this proof comes close to explaining why the rule is true, nor do I consider it particularly attractive (just compare it with Stembridge's self-contained 2-page proof showing a stronger claim, or Gasharov's 4-page proof!); however, it offers a nice survey of interesting connections between combinatorics, representation theory and algebraic geometry (and also Hermitian matrix theory -- Horn's inequalities, to be specific -- which the authors discuss as an aside).
  My errata mostly focus on the Dyck path combinatorics in Section 6 of the article.
  
  
• Errata to Hanspeter Kraft and Claudio Procesi: Classical Invariant Theory - A Primer.
  LaTeX sourcecode of the errata.
  I have read all of this text in 2010 (except for parts of §7.7-7.8) and learnt a lot from it. I hope these errata make reading it somewhat easier.
  
  
• Errata to Victor Kreiman: Products of Factorial Schur Functions.
  LaTeX sourcecode of the errata.
  A nice paper giving (among other things) a generalization of the Bender--Knuth involutions.
  
  
• Errata to Dan Laksov and Anders Thorup: A Determinantal Formula for the Exterior Powers of the Polynomial Ring, Indiana Univ. Math. J. 56 No. 2 (2007), pp. 825--846 (JStor link).
  LaTeX sourcecode of the errata.
  This is an enlightening article connecting symmetric polynomials, exterior powers and universal splitting algebras. Alas, it is not always an easy read. In my errata I attempt to bridge the most nontrivial leaps of logic.
  
  
• Errata to Thomas Lam: A combinatorial generalization of the boson-fermion correspondence (arXiv:math/0507341v1).
  LaTeX sourcecode of the errata.
  This list was made when I was just learning symmetric function theory; I don't think I read the paper completely.
  
  
• Errata to Hartmut Laue: Freie algebraische Strukturen.
  LaTeX sourcecode of the errata.
  Meine Fehlerliste sollte vor allem für Kapitel 1 und 2 nützlich sein.
  
  
• Unofficial re-edition of Hartmut Laue: A graph theoretic proof of the fundamental trace identity, Discrete Mathematics 69 (1988), pp. 197--198, doi:10.1016/0012-365X(88)90019-2.
  LaTeX sourcecode of the re-edition.
  A short note giving a simple combinatorial proof of the fundamental trace identity, a basic result in the theory of PI-algebras.
  
  
• Errata to Lieven Le Bruyn: noncommutative geometry@n, volume 1 : the tools.
  LaTeX sourcecode of the errata.
  The errata cover only the early parts of the first chapter. (Not an algebraic geometer myself, I have read it mainly for the interesting non-standard material it contains on invariant theory. However, I eventually quit reading as it became too hard to follow.)
  
  
• Errata to Marc A. A. van Leeuwen: Schur functions and alternating sums, version of 10 November 2006.
  LaTeX sourcecode of the errata.
  This corrects some mistakes and makes the paper more self-contained (by adding some omitted definitions and proofs).
  
  
• Errata to Marc A. A. van Leeuwen: The Robinson-Schensted and Schützenberger algorithms, an elementary approach, version of 30 January 2013.
  LaTeX sourcecode of the errata.
  This corrects some typos and adds a few details. (I've only read the first half of the paper, though.)
  
  
• Errata to Marc A. A. van Leeuwen: The Littlewood-Richardson rule, and related combinatorics, version of 19 May 2013.
  LaTeX sourcecode of the errata.
  Corrects a few minor imprecisions.
  
  
• Errata to Marc A. A. van Leeuwen: Tableau algorithms defined naturally for pictures, version of 25 November 2011.
  LaTeX sourcecode of the errata.
  For the sake of completeness only (just a few typos are corrected).
  
  
• Errata to Nicholas A. Loehr: Combinatorics, 2nd edition 2018.
  LaTeX sourcecode of the errata.
  One of my favorite textbooks on algebraic and enumerative combinatorics, with a focus on bijective methods. Does not shy away from modern and "expert" viewpoints (e.g., the abacus approach to partitions and rim hooks). The length of the errata list (which was almost entirely produced by GPT) is misleading: almost all the mistakes are trivial to minor.
  
  
• Errata to I. G. Macdonald: Notes on Schubert polynomials, TeXed version 2025.
  LaTeX sourcecode of the errata.
  A classic and well-written introduction to the theory of divided differences and Schubert polynomials (and reduced expressions in symmetric groups). I have only read the first few chapters so far, so these errata don't cover much of the text.
  
  
• Errata to I. G. Macdonald: Schur functions: Theme and variations.
  LaTeX sourcecode of the errata.
  A famous paper that opened new grounds in symmetric functions theory. Apart from a few corrections, these errata fill in many omitted details.
  
  
• Errata to Claudia Malvenuto and Christophe Reutenauer: A Self-Dual Hopf Algebra on Double Partially Ordered Sets, arXiv:0905.3508v1.
  LaTeX sourcecode of the errata.
  This file is a somewhat strange beast: It starts with a list of errata, and ends with me practicing my combinatorics by writing out in gory detail some fairly straightforward arguments (I was just learning about QSym when I read that paper). Note that the published version of the preprint refers to the Hopf algebra as "self-paired" rather than "self-dual", which suggests that the authors had already noticed the first point I was making.
  
  
• Errata to Dominique Manchon: Hopf algebras, from basics to applications to renormalization, arXiv:math/0408405v2.
  LaTeX sourcecode of the errata.
  This contains not only errors, but also alternative proofs which I found nicer than the ones given in the article.
  I can recommend Manchon's exposition. Notice that a version of this paper has also appeared in "Handbook of Algebra" volume 5 (edited by Hazewinkel), but neither version fully contains the other.
  
  
• Errata to Dominique Manchon: A short survey on pre-Lie algebras.
  LaTeX sourcecode of the errata.
  I have only partly read the survey; the main feature of the errata is a detailed proof of the fixed-point iteration lemma that ensures the bijectivity of W in Section 1.1 of the survey.
  
  
• Errata to John W. Moon: Topics on Tournaments, Gutenberg Ebooks 2013.
  LaTeX sourcecode of the errata.
  A classic on the graph theory of tournaments. I have myself only read Section 9, but I let GPT-5.5 hunt for typos and included everything it found that I could confirm.
  
  
• Errata to Philippe Nadeau, Hunter Spink, Vasu Tewari: Schubert polynomial expansions revisited, Forum of Mathematics, Sigma 13 (2025).
  LaTeX sourcecode of the errata.
  This is a delightful article that simplifies and unifies the theories of Schubert polynomials, forest polynomials and slide polynomials under the roof of a general theory that will likely find further uses. I correct some minor errors and add a few details to some computations.
  
  
• Errata to Frederic Patras: La décomposition en poids des algèbres de Hopf, Ann. Inst. Fourier, Grenoble 43, 4 (1993), pp. 1067--1087.
  LaTeX sourcecode of the errata.
  This document is mostly me filling in some details in the classical paper of Patras.
  
  
• Errata to Frederic Patras and Christophe Reutenauer: Higher Lie idempotents, version November 18, 1998.
  LaTeX sourcecode of the errata.
  Apart from corrections of typos and minor errors, these errata close gaps in the proofs of Corollary 4.4 and Theorem 5.4, and remove the dependency on the Poincaré-Birkhoff-Witt theorem.
  
  
• Errata to Nicolas Perrin: Introduction to Kac-Moody Lie algebras.
  LaTeX sourcecode of the errata.
  I have read Chapters 3, 4, 6 of these notes back in 2012 when learning Lie algebra basics. Kac-Moody Lie algebras are not my forte, so treat these with a grain of salt.
  
  
• Errata to Dominique Perrin and Antonio Restivo: Enumerative Combinatorics on Words, chapter in the "Handbook of Combinatorics".
  LaTeX sourcecode of the errata.
  Various imprecisions in the first half of this chapter are corrected (I haven't read the second half yet), and some details are added to the proofs.
  
  
• Errata to Emanuela Petracci: Functional equations and Lie algebras.
  LaTeX sourcecode of the errata.
  Among other things, Petracci gave an explicit basis-free proof of Poincaré-Birkhoff-Witt in characteristic 0. My errata mainly fill in what seems to be a gap in that proof. That said, I might well have misunderstood the proof (it's been one of the first works I've read on the subject).
  
  
• Errata to Joseph Rabinoff: The Theory of Witt Vectors, arXiv:1409.7445v1.
  LaTeX sourcecode of the errata.
  This is a very readable introduction to Witt vectors (both p-typical and general).
  The errata aren't just corrections (there is not very much to correct); they also contain an extra section, which proves a generalization of Theorem 6.6 found by Sam Raskin.
  
  
• Errata to Franco V. Saliola: Hyperplane arrangements and descent algebras, version of 10 January 2006.
  LaTeX sourcecode of the errata.
  Another exposition of Bidigare's proof of Solomon's Mackey formula, using the language of hyperplane arrangements. Also proves some further results on the descent algebra. I correct errors and add a few proofs.
  
  
• Errata to Steven V. Sam: Notes for Math 740 (Symmetric Functions), April 2017.
  LaTeX sourcecode of the errata.
  A brief introduction to symmetric functions, including some tableau combinatorics, a glimpse of Schubert calculus and some basics of Hall-Littlewood polynomials.
  Steven Sam has since updated his notes. Some of my errata still apply.
  
  
• Errata to Alexander Schrijver: A Course in Combinatorial Optimization.
  LaTeX sourcecode of the errata.
  These are corrections and comments on some chapters (mostly 1, 2 and 10) of a highly recommended text that covers (in particular) the basics of polytopes, matchings and matroids. (Beware: I am not an expert on this subject, so I might not have understood everything perfectly.)
  
  
• Errata to Samir Siksek: Introduction to Abstract Algebra.
  LaTeX sourcecode of the errata.
  This is perhaps the most enjoyable introduction into abstract algebra (particularly the basic theory of groups) I know of. (Also, an outdated list of errata to a prior version.)
  
  
• Errata to Samir Siksek: MA377 Rings and Modules.
  LaTeX sourcecode of the errata.
  An introduction to rings and modules with Artin-Wedderburn, Maschke and (a cyclotomic proof of) Little Wedderburn.
  
  
• Errata to Samir Siksek: MA3D5 Galois Theory.
  LaTeX sourcecode of the errata.
  A brief but nice introduction to Galois theory.
  
  
• Errata to Samir Siksek: Lockdown Abstract Algebra.
  LaTeX sourcecode of the errata.
  Some introductory handouts for groups and rings, a kind of teaser for a proper text (see above, by the same author). There was very little to correct here.
  
  
• Errata to Arkadiy Skopenkov: Mathematics via Problems, part 1: Algebra (MSRI/AMS 2021).
  LaTeX sourcecode of the errata.
  An introduction to the theory of algebraic equations as a collection of exercises.
  See also the author's own errata and my review.
  
  
• Errata to Richard Stanley: Algebraic Combinatorics: Walks, Trees, Tableaux, and More, 1st edition, Springer 2013.
  LaTeX sourcecode of the errata.
  This is mostly about Chapter 10 of this (highly recommended) book.
  Warning: A second edition of this book has been published in 2018; it corrects the errors on my list.
  
  
• Errata to Richard Stanley: An Introduction to Hyperplane Arrangements, Geometric Combinatorics (E. Miller, V. Reiner, and B. Sturmfels, eds.), IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, Providence, RI, 2007, pp. 389-496.
  LaTeX sourcecode of the errata.
  Richard Stanley has already incorporated these errata into his own list (which contains many more corrections), but they might nevertheless be of some use since they contain some additional material: a proof of Theorem 3.9, an alternative proof of Theorem 4.11, and some additional details for certain proofs.
  
  
• Errata to Mark Steinberger: Algebra.
  LaTeX sourcecode of the errata.
  Some corrections to a rather deep text on abstract algebra.
  
  
• Errata to Shlomo Sternberg: Lie algebras, 2004.
  LaTeX sourcecode of the errata.
  I have read Chapter 1 of these notes back in 2011.
  
  
• Errata to Neil P. Strickland: The Steinberg module and the Hecke algebra, 2012.
  LaTeX sourcecode of the errata.
  Strickland's highly useful notes cover some basics on the symmetric group (including the Coxeter-Moore presentation), Bruhat cells and parabolic subgroups in GL_n, the classical coset-space definition of the type-A Hecke algebra (in a modern presentation), and the basic properties of the Steinberg module, all in just 15 pages. Unsurprisingly, the proofs are terse and sometimes things are left to the reader. The above errata (apart from correcting typos) fill in some of these missing details, as well as occasionally giving a better (more generalizable or more constructive) proof.
  
  
• Errata to Jessica Striker, Nathan Williams: Promotion and Rowmotion, arXiv:1108.1172v3.
  LaTeX sourcecode of the errata.
  My errata are mainly useful for an alternative (clearer) proof of Lemma 5.1.
  
  
• Errata to Bernd Sturmfels: Algorithms in Invariant Theory, 2nd edition 2004.
  LaTeX sourcecode of the errata.
  This is an inspiring text full of interesting ideas. It might be a bit on the terse side for a first read, but it has much to offer after reading (e.g.) the Kraft/Procesi "primer" or the Draisma/Gijswijt notes (both linked on this page).
  
  
• Errata to Kelli Talaska: Determinants of weighted path matrices, arXiv:1202.3128v1.
  LaTeX sourcecode of the errata.
  I correct some very minor errors in this (highly readable and delightful) preprint. Then I attempt to derive an older result of Talaska (on planar graphs) from the results of this preprint (though I am not sure if my derivation works).
  
  
• Errata to Torsten Ueckerdt: Lecture Notes Combinatorics (2017), 30 May 2017.
  LaTeX sourcecode of the errata.
  Errata for an interesting set of lecture notes on combinatorics.
  
  
• Errata to Mark Wildon: An involutive introduction to symmetric functions.
  LaTeX sourcecode of the errata. [Old version with many errors that have been since corrected by Wildon.]
  A brief introduction to symmetric functions, focussing more strongly on combinatorial methods (sign-reversing involutions in particular).
  
  
• Errata to Mark Wildon: On Bidigare's proof of Solomon's theorem.
  LaTeX sourcecode of the errata.
  A 3-page exposition of Bidigare's proof of Solomon's Mackey formula. Written with the terseness common to British authors, but highly enlightening for those who take the trouble to understand it.
  
  
• Errata to Geordie Williamson: Mind your P- and Q-symbols: Why the Kazhdan-Lusztig basis of the Hecke Algebra is a Cellular Basis, 2004.
  LaTeX sourcecode of the errata.
  This is Williamson's honors thesis, providing a nice elementary introduction to the Robinson-Schensted algorithm and the Kazhdan-Lusztig basis for the type-A Hecke algebra. I have read (most of?) the first 3 sections.
  
  
• OUTDATED Errata to Neil P. Strickland: MAS201 Linear Mathematics.
  The notes cover a semester worth of undergraduate matrix algebra (including applications to Markov chains and differential equations) with rigorous proofs of all important results (including the basic properties of determinants). Highly recommended.
  Warning: These errata are obsolete, as the corrected version of Strickland's notes available from my page corrects them all and some more.
  
  
• OUTDATED Errata to Richard G. Swan: On the straightening law for minors of a matrix, 18 February 2003.
  LaTeX sourcecode of the errata.
  Some corrections to one of the preprints with the highest signal-to-noise ratio I've ever read.
  Warning: Richard Swan has updated his preprint, correcting the errors. (The updated version is available at arXiv:1605.06696.) So these errata are no longer relevant.
  
  

Errata and marginalia

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Darij Grinberg