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Article

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

Discrete Mathematics. 2020. Vol. 343. No. 3.
Talambutsa A., Kolpakov A.

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.