The Spherical Growth Series for Pure Artin Groups of Dihedral Type

Abstract

We consider the kernel of the natural projection from the Artin group of dihedral type $I_2(k)$ to the corresponding Coxeter group, which we call the pure Artin group of dihedral type. We present a rational function expression for the spherical growth series of the pure Artin group of dihedral type with respect to a natural generating set.