2014/05/14 by Henri Mühle, Mühle, Henri
Computer Science · Mathematics · #05E15 (Secondary) #06A07 #20F55 (Primary) #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1405.3522
openalex publication_date 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we give a simple, almost uniform proof that the lattice of noncrossing partitions associated with a well-generated complex reflection group is lexicographically shellable. So far a uniform proof is available only for Coxeter groups. In particular we show that, for any complex reflection group W and any element x∈ W, every x-compatible reflection order is a recursive atom order of the corresponding interval in absolute order. Since any Coxeter element γ in any well-generated complex reflection group admits a γ-compatible reflection order, the lexicographic shellability follows from a well-known result due to Björner and Wachs.