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Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers. (English) Zbl 1485.20100

Summary: 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.

MSC:

20F55 Reflection and Coxeter groups (group-theoretic aspects)
20F36 Braid groups; Artin groups
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