Geodesic
Words with intervening neighbours in infinite Coxeter groups are reduced.
The electronic journal of combinatorics, Tome 17 (2010)
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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 reduced if the group is infinite and irreducible. We present a new and shorter proof using the root automaton for recognition of reduced words.
DOI : 10.37236/458
Classification : 20F55, 05C25, 20F05, 20F10
Mots-clés : intervening neighbours property, Coxeter graphs, root automata, reduced words 
@article{10_37236_458,
     author = {Henrik Eriksson and Kimmo Eriksson},
     title = {Words with intervening neighbours in infinite {Coxeter} groups are reduced.},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/458},
     zbl = {1188.20035},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/458/}
}
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Henrik Eriksson; Kimmo Eriksson. Words with intervening neighbours in infinite Coxeter groups are reduced.. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/458

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