Generating Series for the Coxeter Groups and Applications

Abstract: By forming generating series associated to convenient linear representations of Coxeter groups acting on spaces of constant curvature, we show that the mean values of some related quantities are given by linear recurrence sequences. The tools are the ones used to count words with a given length.

Keywords: representations of Coxeter groups; constant curvature; linear recurrence sequences

Classification (MSC91): 20F55, 51B10, 11J70

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