On the growth of cocompact hyperbolic Coxeter groups - Mathematics > Metric GeometryReport as inadecuate




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Abstract: For an arbitrary cocompact hyperbolic Coxeter group G with finite generatorset S and complete growth function Px-Qx, we provide a recursion formulafor the coefficients of the denominator polynomial Qx which allows todetermine recursively the Taylor coefficients and the pole behavior of thegrowth function of G in terms of its Coxeter subgroup structure. We illustratethis in the easy case of compact right-angled hyperbolic n-polytopes. Finally,we provide detailed insight into the case of Coxeter groups with at most 6generators, acting cocompactly on hyperbolic 4-space, by considering the threecombinatorially different families discovered and classified by Lanner,Kaplinskaya and Esselmann, respectively.



Author: Ruth Kellerhals, Genevieve Perren

Source: https://arxiv.org/



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