Journal article

On the growth of cocompact hyperbolic Coxeter groups

    12.08.2011
Published in:
  • European Journal of Combinatorics. - 2011, vol. 32, no. 8, p. 1299-1316
English For an arbitrary cocompact hyperbolic Coxeter group G with a finite generator set S and a complete growth function fS(x)=P(x)/Q(x), we provide a recursion formula for the coefficients of the denominator polynomial Q(x). It allows us to determine recursively the Taylor coefficients and to study the arithmetic nature of the poles of the growth function fS(x) in terms of its subgroups and exponent variety. We illustrate this in the case of compact right-angled hyperbolic n-polytopes. Finally, we provide detailed insight into the case of Coxeter groups with at most 6 generators, acting cocompactly on hyperbolic 4-space, by considering the three combinatorially different families discovered and classified by Lannér, Kaplinskaya and Esselmann, respectively.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/302142
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