Growth Rates of Coxeter Groups and Perron Numbers

@article{Kolpakov2019GrowthRO,
  title={Growth Rates of Coxeter Groups and Perron Numbers},
  author={Alexander Kolpakov and Alexey Talambutsa},
  journal={arXiv: Group Theory},
  year={2019}
}
We define a large class of abstract Coxeter groups, which we call $\infty$-spanned, for which the word growth rate and the geodesic growth rate appear to be Perron numbers. This class contains a fair amount of Coxeter groups acting on hyperbolic spaces, thus corroborating a conjecture by Kellerhals and Perren. We also show that for this class the geodesic growth rate strictly dominates the word growth rate. 

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CONTENTSIntroductionChapter I. Acute-angled polytopes in Lobachevskii spaces § 1. The Gram matrix of a convex polytope § 2. The existence theorem for an acute-angled polytope with given Gram matrix §
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