Abstract. In this paper we consider the growth rates of -dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the form π k for an integer k ≥ . Combining a classical result by parry with a previous result of ours, we prove that the growth rates of -dimensional hyperbolic Coxeter groups are Perron numbers.
We study the set G of growth rates of of ideal Coxeter groups in hyperbolic 3-space which consists of real algebraic integers greater than 1. We show that (1) G is unbounded above while it has the minimum, (2) any element of G is a Perron number, and (3) growth rates of of ideal Coxeter groups with n generators are located in the closed interval [n − 3, n − 1].2010 Mathematics Subject Classification. Primary 20F55, Secondary 20F65.
In this paper, we construct infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes whose growth rates are Perron numbers. This infinite series is the first example of such a non-compact infinite polytopal series.2010 Mathematics Subject Classification. Primary 20F55, Secondary 20F65.
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