Counting chambers in restricted Coxeter arrangements

2017/06/29 by Tilman Moeller, Gerhard Roehrle, Moeller, Tilman +1
Mathematics · #14N20 #20F55 #52B30 #52C35 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1706.09649

openalex publication_date 2017/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Solomon showed that the Poincaré polynomial of a Coxeter group W satisfies a product decomposition depending on the exponents of W. This polynomial coincides with the rank-generating function of the poset of regions of the underlying Coxeter arrangement. In this note we determine all instances when the analogous factorization property of the rank-generating function of the poset of regions holds for a restriction of a Coxeter arrangement. It turns out that this is always the case with the exception of some instances in type E₈.

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