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Article Dans Une Revue European Journal of Combinatorics Année : 2012

Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers

Résumé

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several examples conclude this work.
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Dates et versions

hal-00699562 , version 1 (21-05-2012)
hal-00699562 , version 2 (26-05-2012)

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Alexander Kolpakov. Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers. European Journal of Combinatorics, 2012, 33 (8), pp.1709-1724. ⟨10.1016/j.ejc.2012.04.003⟩. ⟨hal-00699562v2⟩
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