Words with intervening neighbours in infinite Coxeter groups are reduced
Combinatorics
2008-11-27 v1
Abstract
Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements. Speyer recently proved that words with the intervening neighbours property are irreducible if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of irreducible words.
Keywords
Cite
@article{arxiv.0811.4380,
title = {Words with intervening neighbours in infinite Coxeter groups are reduced},
author = {Henrik Eriksson and Kimmo Eriksson},
journal= {arXiv preprint arXiv:0811.4380},
year = {2008}
}