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On the growth of cocompact hyperbolic Coxeter groups

Kellerhals, Ruth ; Perren, Geneviève

In: European Journal of Combinatorics, 2011, vol. 32, no. 8, p. 1299-1316

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...