Results 31 to 40 of about 157 (62)
Chow rings of matroids as permutation representations
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincaré duality and the Hard Lefschetz theorem.
Robert Angarone +2 more
wiley +1 more source
ℓp$\ell ^p$ metrics on cell complexes
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Motivated by the observation that groups can be effectively studied using metric spaces modelled on ℓ1$\ell ^1$, ℓ2$\ell ^2$ and ℓ∞$\ell ^\infty$ geometry, we consider cell complexes equipped with an ℓp$\ell ^p$ metric for arbitrary p$p$. Under weak conditions that can be checked locally, we establish non‐positive curvature properties of these
Thomas Haettel, Nima Hoda, Harry Petyt
wiley +1 more source
Metric spaces in chess and international chess pieces graph diameters
, 2023 This paper aims to study the graph radii and diameters induced by the $k$-dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times \dots \times n\} \subseteq \mathbb{Z}^k$ lattice since they originate as ...
Ripà, Marco
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Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.Abstract Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$, the m$m$‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$. The classical Shi arrangement (m=0$m=0$) was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for W$W$.
Matthew Dyer +3 more
wiley +1 more source
Topological methods in zero-sum Ramsey theory
, 2023 A cornerstone result of Erd\H os, Ginzburg, and Ziv (EGZ) states that any sequence of $2n-1$ elements in $\mathbb{Z}/n$ contains a zero-sum subsequence of length $n$.
Duke, Jacob Lehmann +7 more
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Rational cross‐sections, bounded generation, and orders on groups
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We provide new examples of groups without rational cross‐sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Our examples contain a finitely presented HNN‐extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word
Corentin Bodart
wiley +1 more source
Relatively Anosov representations via flows II: Examples
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract This is the second in a series of two papers that develops a theory of relatively Anosov representations using the original “contracting flow on a bundle” definition of Anosov representations introduced by Labourie and Guichard–Wienhard. In this paper, we focus on building families of examples.
Feng Zhu, Andrew Zimmer
wiley +1 more source
COMBINATORIAL ASPECTS OF EXCEDANCES AND THE FROBENIUS COMPLEX [PDF]
, 2011 In this dissertation we study the excedance permutation statistic. We start by extending the classical excedance statistic of the symmetric group to the affine symmetric group eSn and determine the generating function of its distribution.
Clark, Eric Logan
core +2 more sources
Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams
, 2018 We investigate the Castelnuovo--Mumford regularity and the multiplicity of the toric ring associated to a three-dimensional Ferrers diagram. In particular, in the rectangular case, we are able to provide direct formulas for these two important invariants.
Lin, Kuei-Nuan, Shen, Yi-Huang
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New Perspectives of Quantum Analogues [PDF]
, 2016 In this dissertation we discuss three problems. We first show the classical q-Stirling numbers of the second kind can be expressed more compactly as a pair of statistics on a subset of restricted growth words.
Cai, Yue
core +1 more source