Growth Rates of 3-dimensional Hyperbolic Coxeter Groups are Perron Numbers

Yukita, Tomoshige

Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 405-422

Résumé

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the form $\frac{\pi }{k}$ for an integer $k\ge 7$ . Combining a classical result by Parry with a previous result of ours, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.

Détail

DOI : 10.4153/CMB-2017-052-5

Mots-clés : 20F55, 20F65, Coxeter group, growth function, growth rate, Perron number

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