Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers
arXiv:1105.6267
Abstract
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.
26 pages, 16 figures, 4 data tables; minor corrections; European Journal of Combinatorics, 2012