Kellerhals, Ruth Perren, Geneviève 2011-08-12 For an arbitrary cocompact hyperbolic Coxeter group <i>G</i> with a finite generator set <i>S</i> and a complete growth function <i>f</i>_<i>S</i>(<i>x</i>)=<i>P</i>(<i>x</i>)/<i>Q</i>(<i>x</i>), we provide a recursion formula for the coefficients of the denominator polynomial <i>Q</i>(<i>x</i>). It allows us to determine recursively the Taylor coefficients and to study the arithmetic nature of the poles of the growth function <i>f</i>_<i>S</i>(<i>x</i>) in terms of its subgroups and exponent variety. We illustrate this in the case of compact right-angled hyperbolic <i>n</i>-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. application/pdf https://folia.unifr.ch/global/documents/302142 https://folia.unifr.ch/documents/302142/files/kel_gch.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ejc.2011.03.020 info:eu-repo/semantics/openAccess License undefined European Journal of Combinatorics. - 2011, vol. 32, no. 8, p. 1299-1316 info:eu-repo/classification/udc/51 On the growth of cocompact hyperbolic Coxeter groups http://purl.org/coar/resource_type/c_6501