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arXiv · 1809.09591

Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers

Alexander Kolpakov·Alexey Talambutsa
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Abstract

We prove that for any infinite right-angled Coxeter or Artin group, its spherical and geodesic growth rates (with respect to the standard generating set) either take values in the set of Perron numbers, or equal $1$. Also, we compute the average number of geodesics representing an element of given word length in such groups.

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Alexander Kolpakov, Alexey Talambutsa. 2018-09-25. Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers. https://arxiv.org/abs/1809.09591

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