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

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.