Michihiko Fujii

The Spherical Growth Series for Pure Artin Groups of Dihedral Type

We consider the kernel of the natural projection from the Artin group of dihedral type I2(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. 2010 Mathematics Subject Classification: Primary20F36,20F05,20F10;Secondary68R15.

The growth rates for pure Artin groups of dihedral type

We consider the kernel of the natural projection from the Artin group of dihedral type I2(k) to the associated Coxeter group, which we call a pure Artin group of dihedral type and write PI2(k). We show that the growth rates for both the spherical growth series and geodesic growth series of PI2(k) with respect to a natural generating set are Pisot numbers. 2010 Mathematics Subject Classication : Primary 20F36, 20F05, 20F65, 26A12; Secondary 68R15, 11R06.