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2009 Automatic growth series for right-angled Coxeter groups
Rebecca Glover, Richard Scott
Involve 2(4): 371-385 (2009). DOI: 10.2140/involve.2009.2.371

Abstract

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.

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Rebecca Glover. Richard Scott. "Automatic growth series for right-angled Coxeter groups." Involve 2 (4) 371 - 385, 2009. https://doi.org/10.2140/involve.2009.2.371

Information

Received: 11 March 2008; Revised: 8 September 2009; Accepted: 26 September 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1223.20030
MathSciNet: MR2579557
Digital Object Identifier: 10.2140/involve.2009.2.371

Subjects:
Primary: 05A15, 20F10, 20F55

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.2 • No. 4 • 2009
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