Words with intervening neighbours in infinite Coxeter groups are reduced

Details Words with intervening neighbours in infinite Coxeter groups are reduced Words with intervening neighbours in infinite Coxeter groups are reduced

2008-11-26

arxiv.org/abs/0811.4380v1

Mathematics

Combinatorics

Scientific paper

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.

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