Cycles in subexpression graphs

2025/06/12 by Vladimir Shchigolev, Shchigolev, Vladimir
Computer Science · #05C45 #20F55 #51F15 #57M15 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.11208

openalex publication_date 2025/06/12 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

Let \mathfrakS(\underlines,w) be the graph whose vertices are all subexpressions with target w of a fixed expression \underlines in generators of a Coxeter group and edges are the pairs of subexpressions with Hamming distance 2. We prove that \mathfrakS(\underlines,w) is connected and its cycle space is spanned by cycles of lengths d+2, where d ranges over all positive divisors of all finite orders of products of at most two entries of \underlines.

Citations

• Galleries for root subsystems
• Categories of Bott-Samelson varieties
• Imaginary cone and reflection subgroups of Coxeter groups
• Semidirect product decomposition of Coxeter groups
• Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux
• The fibre of the Bott-Samelson Resolution

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• Forbidden cycles in metrically homogeneous graphs
• On distance two in Cayley graphs of Coxeter groups
• Sharp thresholds for spanning regular subgraphs
• Solution to a BCC 2022 problem