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Yukita, Tomoshige
Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers
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 $k\geq{7}$. 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.

Keywords:Coxeter group, growth function, growth rate, Perron number
Categories:20F55, 20F65

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