Ricci curvature of Bruhat orders

2021/03/05 by Viola Siconolfi, Siconolfi, Viola
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Artin group #Bruhat order #Combinatorics #Combinatorics (math.CO) #Coxeter complex #Coxeter group #Curvature #FOS: Mathematics #Geometry #Graph #Homotopy and Cohomology in Algebraic Topology #Longest element of a Coxeter group #Mathematics #Pure mathematics #Ricci curvature #Weyl group #math.CO

paper · pdf · doi:10.48550/arxiv.2103.03828

published in arXiv (Cornell University) (Cornell University) · 32 pages

arxiv created 2021/03/05 · openalex publication_date 2021/03/05 · arxiv updated 2021/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study the Ricci curvature of the Hasse diagrams of the Bruhat order of finite irreducible Coxeter groups. For this purpose we compute the maximum degree of these graphs for types B_n and D_n. The proof uses a new graph Γ(π) defined for any element π in the corresponding group.

Related

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• Graphs with nonnegative Ricci curvature and maximum degree at most 3
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• On Degrees in the Hasse Diagram of the Strong Bruhat Order
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