2021/09/13 by Axel Hultman, Hultman, Axel, Vincent Umutabazi +1
Computer Science · Mathematics · #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2109.05832
openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 |S| - 1. In addition, we find simple recurrence formulas for the number of spheres in the wedge.