Conjugacy classes of cyclically fully commutative elements in Coxeter groups of type A

2015/06/07 by Brooke Fox, Fox, Brooke
Mathematics · #06A07 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:06A07 #msc:20F55

paper · pdf · doi:10.48550/arxiv.1506.02299

Author's M.S. Thesis (2014) directed by D.C. Ernst at Northern Arizona University. 53 pages, 47 figures. New version adds reference to arXiv:1403.1130. arXiv admin note: text overlap with arXiv:1202.6657 by other authors

arxiv created 2015/06/23 · arxiv updated 2015/06/24

Abstract

In this thesis, we study the combinatorics of cyclically fully commutative elements in Coxeter groups of type A as it relates to conjugacy. In particular, we introduce the notion of cylindrical heaps and ring equivalence in order to state our main result, which says that two cyclically fully commutative elements of a Coxeter group of type A are conjugate if and only if their corresponding cylindrical heaps are ring equivalent.

Citations

• Characterization of Cyclically Fully commutative elements in finite and affine Coxeter Groups

Related

• Characterization of Cyclically Fully commutative elements in finite and affine Coxeter Groups
• Structure of conjugacy classes in Coxeter groups
• Toric heaps, cyclic reducibility, and conjugacy in Coxeter groups
• Fully commutative elements in finite and affine Coxeter groups
• Combinatorics of fully commutative involutions in classical Coxeter groups