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arXiv · 0811.4380

Words with intervening neighbours in infinite Coxeter groups are reduced

Henrik Eriksson·Kimmo Eriksson
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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.

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Henrik Eriksson, Kimmo Eriksson. 2008-11-26. Words with intervening neighbours in infinite Coxeter groups are reduced. https://arxiv.org/abs/0811.4380

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