English

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}
}