Vol. 2, No. 4, 2009

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Automatic growth series for right-angled Coxeter groups

Rebecca Glover and Richard Scott

Vol. 2 (2009), No. 4, 371–385

Right-angled Coxeter groups have a natural automatic structure induced by their action on a CAT(0) cube complex. The normal form for this structure is defined with respect to the generating set consisting of all cliques in the defining graph for the group. In this paper we study the growth series for right-angled Coxeter groups with respect to this automatic generating set. In particular, we show that there exist nonisomorphic Coxeter groups with the same automatic growth series, and give a comparison with the usual growth series defined with respect to the standard generating set.

Coxeter groups, growth series
Mathematical Subject Classification 2000
Primary: 05A15, 20F10, 20F55
Received: 11 March 2008
Revised: 8 September 2009
Accepted: 26 September 2009
Published: 28 October 2009

Communicated by Vadim Ponomarenko
Rebecca Glover
Department of Mathematics
The University of North Carolina
CB No. 3250, Phillips Hall
Chapel Hill, NC 27599-3250
United States
Richard Scott
Department of Mathematics and Computer Science
Santa Clara University
500 El Camino Real
Santa Clara, CA 95053-0290
United States