Diameter of reduced words
arXiv:0906.4768
Abstract
For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to supersolvable hyperplane arrangements.
Version 4 points out a gap in the proof of Theorem 4.9, filled in work of T. McConville (arXiv:1411.1305)