## Involve: A Journal of Mathematics

• Involve
• Volume 2, Number 4 (2009), 371-385.

### Automatic growth series for right-angled Coxeter groups

#### 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.

#### Article information

Source
Involve, Volume 2, Number 4 (2009), 371-385.

Dates
Revised: 8 September 2009
Accepted: 26 September 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513799185

Digital Object Identifier
doi:10.2140/involve.2009.2.371

Mathematical Reviews number (MathSciNet)
MR2579557

Zentralblatt MATH identifier
1223.20030

Keywords
Coxeter groups growth series

#### Citation

Glover, Rebecca; Scott, Richard. Automatic growth series for right-angled Coxeter groups. Involve 2 (2009), no. 4, 371--385. doi:10.2140/involve.2009.2.371. https://projecteuclid.org/euclid.involve/1513799185

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