Errata and marginalia
This is an archive of my comments and corrections on other authors'
mathematical works.
This includes lists of errata, alternative proofs, omitted details
and the occasional (simple) generalization.
Caveat lector: Do not take my lists of errata at face value.
There is no guarantee that what I claim to be errors are actually errors,
nor that what I believe to be corrections is more correct than the
originals.
If you have comments on my comments, please let me know at
A@B.com, where A = darijgrinberg and B = gmail.
If you are looking for my errata for elementary geometry books,
they are elsewhere.

Unofficial
reedition
of J. Désarménien, Joseph P. S. Kung, GianCarlo Rota: Invariant Theory, Young
Bitableaux, and Combinatorics,
Advances in Mathematics, Volume 27, Issue
1, January 1978, pp. 6392,
doi:10.1016/00018708(78)900774.
LaTeX sourcecode of the reedition.
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 characteristicfree and partly combinatorial.
The reedition corrects various errors as well as adding
details to the proofs.

Translation (with corrections)
of Jacques Désarménien: Modulon 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.

Errata
to Steven V. Sam: Notes for Math 740 (Symmetric Functions).
LaTeX sourcecode of the errata.
A brief introduction to symmetric functions, including some
tableau combinatorics, a glimpse of Schubert calculus and some
basics of HallLittlewood polynomials.

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.]
Another brief introduction to symmetric functions, focussing more
strongly on combinatorial methods (signreversing involutions in particular).

Errata
to David M. Goldschmidt: Group Characters, Symmetric Functions, and
the Hecke Algebra. (Apparently currently inaccessible from the AMS
site.
Makeshift
archive.org link.)
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 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.
Besides a long list of typos, I have written a few notes on the subject
(warning: undergraduate work, not very polished).

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 (characteristic0) 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 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
§7.77.8) and learnt a lot from it. I hope these errata make
reading it somewhat easier.

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 SchurWeyl duality in Section 11.1. I have not read it
in full, but the errata cover a significant part of the text.

Errata
to Torsten Ueckerdt:
Lecture Notes Combinatorics (2017).
LaTeX sourcecode of the errata.
Errata for an interesting set of lecture notes on combinatorics.

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 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 nonstandard material it contains on invariant theory.
However, I eventually quit reading as it became too hard to follow.)

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 wellwritten, educational and enjoyable, if lacking proofreading);
most importantly, it documents a gap in the proof of Theorem 6.5.8 (which
I don't know how to fix).

Errata
to Shlomo Sternberg: Lie algebras.
LaTeX sourcecode of the errata.
I have read Chapter 1 of these notes back in 2011.

Errata
to Nicolas Perrin: Introduction to KacMoody 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.
KacMoody Lie algebras are not my forte, so treat these with a grain of salt.

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 Valentin Féray:
Approche Duale des représentations du groupe symétrique.
LaTeX sourcecode of the errata.
Corrections to algebraic/combinatorial parts of these nice notes.

Errata
to Hartmut Laue:
Freie algebraische Strukturen.
LaTeX sourcecode of the errata.
Meine Fehlerliste sollte vor allem für Kapitel 1 und 2 nützlich sein.

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, however, that some of these comments are probably due to my
misunderstanding of the text  I am far from an expert on combinatorial
optimization.)

Errata
to William CrawleyBoevey: Cohomology and Central Simple Algebras.
LaTeX sourcecode of the errata.
There was not much to correct here, so this is just for the sake of completeness.

Errata
to Jessica Striker, Nathan Williams: Promotion and Rowmotion, arXiv:1108.1172v3.
LaTeX sourcecode of the errata.
Mainly useful for an alternative (clearer) proof of Lemma 5.1.

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 RogersRamanujan identities
(via a finitary version).

Errata
to Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello: Noncommutative determinants, CauchyBinet formulae, and Capellitype 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
allminors Cayley identity using the tools in the paper).

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 Roger Howe and Soo Teck Lee: Why should the Littlewoodâ€“Richardson rule be true?.
LaTeX sourcecode of the errata.
This article (which I have never read in full)
proves the LittlewoodRichardson rule on about 40 pages, and the
proof is far from selfcontained (it relies on standard monomial
theory and some invariant theory).
Unlike its authors, 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 selfcontained 2page proof showing a stronger claim, or
Gasharov's 4page 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 P. Fleischmann: A New Degree Bound for Vector Invariants of Symmetric Groups.
LaTeX sourcecode of the errata.
Minor corrections to a nice and useful article.

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 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 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. 825846.
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 Sergey Fomin and Curtis Greene: Noncommutative Schur functions and their applications,
Discrete Mathematics 306 (2006), pp. 1080â€“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 Neil P. Strickland: The Steinberg module and the Hecke algebra.
LaTeX sourcecode of the errata.
Strickland's highly useful notes cover
some basics on the symmetric group
(including the CoxeterMoore presentation),
Bruhat cells and parabolic subgroups in GL_{n},
the classical cosetspace definition of the typeA 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.

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 Samir Siksek: Introduction to Abstract Algebra.
This is perhaps the most enjoyable introduction into abstract
algebra (particularly the basic theory of groups) I know of.
Most corrections are trivial.

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
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. 15371546.
This corrects the proof of the bijectivity of the GesselReutenauer
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. 189215.
This corrects the proof of the welldefinedness of the GesselReutenauer
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 JacobiTrudi identities.)

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 selfcontained (by
adding some omitted definitions and proofs).

Errata
to Marc A. A. van Leeuwen: The RobinsonSchensted 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 LittlewoodRichardson 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 Mark Wildon: On Bidigare's proof of Solomon's theorem.
LaTeX sourcecode of the errata.
A 3page exposition of Bidigare's proof of Solomon's Mackey formula.
Written with the terseness common to British authors,
but highly enlightening if you can understand it :)

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.
Proves some further results as well.
I correct errors and add a few proofs.

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 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 Dominique Manchon: Hopf algebras, from basics to applications to renormalization, version v2 (2006).
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 none of the two versions fully contains the
other.

Errata
to S. Gill Williamson: The commonsubmatrix Laplace expansion.
LaTeX sourcecode of the errata.
Errata for a nice elementary proof of the "commonsubmatrix Laplace expansion".

Errata
to Pavel Etingof and Xiaoguang Ma:
Lecture Notes on Cherednik Algebras.
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, I never got past page 10, when it started really
going over my
head...) The "errata" include an alternative proof of Proposition 2.18
which uses no transcendental methods (but takes nearly 20 pages of
computation).

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
signaltonoise 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
to Vesselin Gasharov: A short proof of the LittlewoodRichardson rule, 27 August 1998.
LaTeX sourcecode of the errata.
Corrections to a classical paper in symmetric functions theory.

Errata
to Loic Foissy and Claudia Malvenuto: The Hopf algebra of finite topologies and Tpartitions, 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 130169); 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 FoissyMalvenuto 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 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 ptypical 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 Richard Stanley: Algebraic Combinatorics: Walks, Trees, Tableaux, and More, 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. 389496.
LaTeX sourcecode of the errata.
Richard Stanley has already incorporated these errata in his own file (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 that I found lacking in proofs (a subjective judgment).

Errata
to Alexander E. Holroyd, Lionel Levine, Karola Mészáros, Yuval Peres, James Propp and David B. Wilson: ChipFiring and RotorRouting 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 HolroydLevineMészárosPeresProppWilson 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 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 ComesOstrik 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 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
what I believe to be a gap in the proof of Theorem 5.4, and
along the way generalize some results in the paper.
Unfortunately I was not able to understand how Corollary 4.4 is proven.
Any help is welcome!

Errata
to Frederic Patras: La décomposition en poids des algèbres de Hopf, Ann. Inst. Fourier, Grenoble 43, 4 (1993), pp. 10671087.
LaTeX sourcecode of the errata.
This document is mostly me filling in some details in the classical
paper of Patras.

Errata
to F. G. Friedlander, M. Joshi:
Introduction to the theory of distributions
(Google Books link).
This is a list of mistakes I caught in the first chapters (mostly 15
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.)
 Darij Grinberg, FultonHarris
Proposition 15.15 (in German)
(Version 29. Januar 2011).
PDFDatei; siehe auch TeXQuellcode.
Ein Beweis, daß die Darstellung von GL(V), die man durch
SchurWeylDualität aus der irreduziblen Darstellung c_{λ}ℂ[S_{m}]
von
S_{m}
erhält, als Darstellung der Liealgebra sl(V) das höchste Gewicht λ_{1}L_{1}
+ λ_{2}L_{2} + ... + λ_{n}L_{n} hat
(wenn die CartanUnteralgebra und die Weylkammer "richtig" gewählt
wird). Dies ist Proposition 15.15 in FultonHarris, wo ein nicht ganz
richtiger Beweis gegeben wird. Der Beweis hier versucht, diesen Fehler
zu vermeiden.
Errata and marginalia
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Darij Grinberg