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Adian 90: Conference on Mathematical Logic, Algebra, and Computation
July 5, 2021 16:15–17:00, Moscow, Steklov Mathematical Institute of RAS (Moscow) and online in Zoom

Growth rates of Coxeter groups and Perron numbers

A. L. Talambutsa

Steklov Mathematical Institute, Moscow
 Video records: MP4 2,692.6 Mb

We define a large class of abstract Coxeter groups, that we call $\infty$–spanned, and for which we prove that the word growth rate and the geodesic growth rate are Perron numbers. This class contains a fair amount of Coxeter groups acting on hyperbolic spaces, including a notable example of Vinberg and Kaplinskaya of a cofinite 50-generated group which acts on the 19-dimensional hyperbolic space. In order to overcome the computational difficulties, instead of Steinberg formula, we use finite automata constructed by Brink and Howlett and Perron-Frobenius theory.