Old recurrence formulae for growth series of Coxeter groups

TL;DR

This paper presents new proofs of classical formulas for Coxeter group growth series by leveraging the structures of Coxeter, Davis, and Tits complexes, offering fresh insights into their geometric and algebraic properties.

Contribution

It introduces novel proof techniques for existing growth series formulas using geometric complexes associated with Coxeter groups.

Findings

Classical growth series formulas are proved using complex structures.

New proof methods provide deeper geometric understanding.

Results unify algebraic and geometric perspectives on Coxeter groups.

Abstract

Several classical formulae for the growth series of a Coxeter group are proved in a new way, using the structure of the Coxeter complex, the Davis complex, or the Tits non-complex.