对合的布尔复形

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2022-12-28 DOI:10.1007/s00026-022-00629-9

Axel Hultman, Vincent Umutabazi

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引用次数: 0

摘要

设（W，S）是一个Coxeter系统。我们引入了W的对合布尔复形，它是Ragnarsson和Tenner研究的W的布尔复形的一个类似物。通过应用离散Morse理论，我们确定了一大类（W，S）（包括所有有限Coxeter群）对合布尔复形的同伦型，发现该同伦型是一个维数为\（\vert S\vert-1\）的球楔的同伦类型。此外，我们还找到了楔中球体数量的简单递推公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Boolean Complexes of Involutions

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Boolean Complexes of Involutions

Let (W, S) be a Coxeter system. We introduce the boolean complex of involutions of W which is an analogue of the boolean complex of W studied by Ragnarsson and Tenner. By applying discrete Morse theory, we determine the homotopy type of the boolean complex of involutions for a large class of (W, S), including all finite Coxeter groups, finding that the homotopy type is that of a wedge of spheres of dimension \(\vert S\vert -1\). In addition, we find simple recurrence formulas for the number of spheres in the wedge.

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches