2012/06/30 by Edward Richmond, William Slofstra · 11 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Artin group #Combinatorics #Coxeter complex #Coxeter element #Coxeter group #Factorization #Geometric and Algebraic Topology #Group (periodic table) #Longest element of a Coxeter group #Mathematics #Pure mathematics #Rank (graph theory) #Type (biology) #math.AG #math.CO #msc:05E15 #msc:20F55
paper · pdf · doi:10.1007/s10801-013-0460-y
published in Journal of Algebraic Combinatorics 39(3), 659-681 (Springer Science+Business Media) · 22 pages, 3 figures, version 3: Section 3.3 is now its own Section 4. New Lemma 2.3 on a property of BP-decompositions. Proof of Corollary 3.7 added. Notation changes made for descents sets (S->D). Several other minor changes
arxiv created 2013/03/14 · openalex publication_date 2013/07/12 · arxiv updated 2014/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a family of infinite-type Coxeter groups defined by the avoidance of certain rank 3 parabolic subgroups. For this family, rationally smooth elements can be detected by looking at only a few coefficients of the Poincaré polynomial. We also prove a factorization theorem for the Poincaré polynomial of rationally smooth elements. As an application, we show that a large class of infinite-type Coxeter groups have only finitely many rationally smooth elements. Explicit enumerations and descriptions of these elements are given in special cases.