Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers
classification
🧮 math.GT
keywords
coxeterdimensionalgrowthhyperbolicratescitegroupsnumbers
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In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra some of its dihedral angles are $\frac{\pi}{m}$ for $m\geq{7}$. By combining with the classical result by Parry \cite{Pa} and the main result of \cite{Y}, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.
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