Data about hyperbolic Coxeter systems

2015/03/30 by T. Terragni, Terragni, T.
Mathematics · #20F55 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F55

paper · pdf · doi:10.48550/arxiv.1503.08764

86 pages, dataset

arxiv created 2015/03/30 · arxiv updated 2015/03/31

Abstract

We collect several data about Coxeter systems (cf. [Bou07, Hum90]), with particular emphasis on the hyperbolic ones. For each (\preceq-minimal) hyperbolic Coxeter system (W,S) the Poincaré series p_(W,S)(t)=∑_{w∈ W} t^ℓ(w) and the growth rate ω(W,S)=\limsup_n √[n]a_n are explicitly computed using Magma (cf. [BCP97]). These computations were performed in connection to the proof of [Ter, Thm. B]. Since the Poincaré series represents a rational function, one may recover the sequence (a_k)_{k≥ 0} through a linear recurrence relation on the coefficients, provided that enough terms at the beginning of the sequence are known. For each Coxeter system the initial coefficients (a_k)_k=0^N are computed, where N is the degree of the numerator of p_(W,S)(t).

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