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Automatic growth
series for right-angled Coxeter groups
Rebecca Glover and Richard Scott
Vol. 2 (2009), No. 4, 371–385
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Abstract |
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Right-angled Coxeter groups have a natural automatic structure induced by their action on a CAT() 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. |
Keywords
Coxeter groups, growth series
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Mathematical Subject Classification 2000
Primary: 05A15, 20F10, 20F55
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Milestones
Received: 11 March 2008
Revised: 8 September 2009
Accepted: 26 September 2009
Published: 28 October 2009
Communicated by Vadim Ponomarenko
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Authors |
| Rebecca Glover | |
| Department of Mathematics The University of North Carolina CB No. 3250, Phillips Hall Chapel Hill, NC 27599-3250 United States |
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| Richard Scott | |
| Department of Mathematics and
Computer Science Santa Clara University 500 El Camino Real Santa Clara, CA 95053-0290 United States |
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| http://schubert.scu.edu/rscott | |
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