Diameters of graphs of reduced words and rank-two root subsystems

Abstract

We study the diameter of the graph $G(w)$ of reduced words of an element $w$ in a Coxeter group $W$ whose edges correspond to applications of the Coxeter relations. We resolve conjectures of Reiner--Roichman and Dahlberg--Kim by proving a tight lower bound on this diameter when $W=S_n$ is the symmetric group and by characterizing the equality cases. We also give partial results in other classical types which illustrate the limits of current techniques.

14 pages, comments welcome

Cited by in corpus (1)

• Extending a word property for twisted Coxeter systems