Results 111 to 120 of about 55,778 (257)
Hopf Algebras in Combinatorics
, 2014 These notes -- originating from a one-semester class by their second author at the University of Minnesota -- survey some of the most important Hopf algebras appearing in combinatorics. After introducing coalgebras, bialgebras and Hopf algebras in general, we study the Hopf algebra of symmetric functions, including Zelevinsky's axiomatic ...
Grinberg, Darij, Reiner, Victor
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Faber's socle intersection numbers via Gromov–Witten theory of elliptic curve
Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2698-2707, September 2025.Abstract The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of Mg$\mathcal {M}_g$. This new proof exhibits a new beautiful tautological relation that stems from the recent work of Oberdieck–Pixton on the Gromov–Witten theory of the elliptic curve via a refinement of ...
Xavier Blot +2 more
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Topology of matching complexes of complete graphs via discrete Morse theory [PDF]
Discrete Mathematics & Theoretical Computer ScienceBouc (1992) first studied the topological properties of $M_n$, the matching complex of the complete graph of order $n$, in connection with Brown complexes and Quillen complexes. Bj\"{o}rner et al. (1994) showed that $M_n$ is homotopically $(\nu_n-1)$
Anupam Mondal +2 more
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Loops, matchings and alternating-sign matrices [PDF]
, 2003 The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain classes of ...
de Gier, Jan
core
Blow-up algebras in Algebra, Geometry and Combinatorics
, 2019 Programa de Doctorat en Matemàtica i ...
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Geometric realizations of the s‐weak order and its lattice quotients
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract For an n$n$‐tuple s${\bm{s}}$ of nonnegative integers, the s${\bm{s}}$‐weak order is a lattice structure on s${\bm{s}}$‐trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the forcing order of the s${\bm{s}}$‐weak order in terms of combinatorial objects ...
Eva Philippe, Vincent Pilaud
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HIGHER ALGEBRA IN COMBINATORICS
, 2023 This article has easy and a very nice application on how to solve elementary combinatorics problems using linear ...
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Combinatorics of rooted trees and Hopf algebras [PDF]
Transactions of the American Mathematical Society, 2003 We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of non-root vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator is the operator that multiplies a rooted tree by its number of ...
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Splines on Cayley graphs of the symmetric group
Forum of Mathematics, SigmaA spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a ring. We consider
Nathan R. T. Lesnevich
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On the Lehmer conjecture and counting in finite fields
Discrete Analysis, 2019 On the Lehmer conjecture and counting in finite fields, Discrete Analysis 2019:5, 8pp. Let $\alpha$ be an algebraic number and let $a_0\prod_{i=1}^k(x-\alpha_i)$ be its minimal polynomial. The _Mahler measure_ of $\alpha$ is defined to be the quantity $|
Emmanuel Breuillard, Peter Pal Varju
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