Diameter of reduced words
Combinatorics
2020-06-03 v4 Geometric Topology
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.
Cite
@article{arxiv.0906.4768,
title = {Diameter of reduced words},
author = {Victor Reiner and Yuval Roichman},
journal= {arXiv preprint arXiv:0906.4768},
year = {2020}
}
Comments
Version 4 points out a gap in the proof of Theorem 4.9, filled in work of T. McConville (arXiv:1411.1305)