Old recurrence formulae for growth series of Coxeter groups
Jan Dymara

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.
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