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arXiv · 2209.05100

Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers

Naomi Bredon·Tomoshige Yukita
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Abstract

In this paper, we study growth rates of Coxeter systems with Davis complexes of dimension at most $2$. We show that if the Euler characteristic $\chi$ of the nerve of a Coxeter system is vanishing (resp. positive), then its growth rate is a Salem (resp. a Pisot) number. In this way, we extend results due to Floyd and Parry. Moreover, in the case where $\chi$ is negative, we provide infinitely many non-hyperbolic Coxeter systems whose growth rates are Perron numbers.

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Naomi Bredon, Tomoshige Yukita. 2022-09-12. Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers. https://doi.org/10.2140/agt.2024.24.1787

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