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Abelian Combinatorics on Words: a Survey [PDF]
, 2022 We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on \emph{abelian equivalence}, which is the equivalence relation defined in the set of words by having the same Parikh vector ...
arxiv +1 more source
The combinatorics of Jeff Remmel [PDF]
arXiv, 2021 We give a brief overview of the life and combinatorics of Jeff Remmel, a mathematician with successful careers in both logic and combinatorics.
arxiv
A determinacy approach to Borel combinatorics [PDF]
J. Amer. Math. Soc. 29 (2016), 579-600, 2013 We introduce a new method, involving infinite games and Borel determinacy, which we use to answer several well-known questions in Borel combinatorics.
arxiv +1 more source
Enumerative and Algebraic Combinatorics in the 1960's and 1970's [PDF]
arXiv, 2021 A partly autobiographical survey of the development of enumerative and algebraic combinatorics in the 1960's and 1970's.
arxiv
Borel chain conditions of Borel posets [PDF]
arXiv, 2021 We study the coarse classification of partial orderings using chain conditions in the context of descriptive combinatorics. We show that (unlike the Borel counterpart of many other combinatorics), we have a distinct hierarchy of different chain conditions, similar to the classical case.
arxiv
Lecture notes on algebraic methods in combinatorics [PDF]
arXiv, 2023 These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were presented in the course.
arxiv
Combinatorics and N-Koszul algebras [PDF]
arXiv, 2009 The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.
arxiv
Refuting conjectures in extremal combinatorics via linear programming [PDF]
arXiv, 2019 We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics.
arxiv
Pythagorean Hyperplane Arrangements: Combinatorics of Gain Genericity [PDF]
arXiv, 2023 We study Pythagorean hyperplane arrangements, originally defined by Zaslavsky. In this first part of a series on such arrangements, we introduce a new notion of genericity for such arrangements. Using this notion we construct an auxiliary hyperplane arrangement whose combinatorics determines the combinatorics of all possible Pythagorean arrangements ...
arxiv
A structural approach to subset-sum problems [PDF]
arXiv, 2008 We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various areas, such as number theory, combinatorics and mathematical physics.
arxiv