Abstract
We study the set $\mathcal{G}$ of growth rates of ideal Coxeter groups in hyperbolic 3-space; this set consists of real algebraic integers greater than 1. We show that (1) $\mathcal{G}$ is unbounded above while it has the minimum, (2) any element of $\mathcal{G}$ is a Perron number, and (3) growth rates of ideal Coxeter groups with $n$ generators are located in the closed interval $[n-3, n-1]$.
Citation
Yohei Komori. Tomoshige Yukita. "On the growth rate of ideal Coxeter groups in hyperbolic 3-space." Proc. Japan Acad. Ser. A Math. Sci. 91 (10) 155 - 159, December 2015. https://doi.org/10.3792/pjaa.91.155
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