Title The Spherical Growth Series for Pure Artin Groups of DihedralType
نویسنده
چکیده
In this paper, 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.
منابع مشابه
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 Classification...
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We consider the Artin groups of dihedral type I2(k) defined by the presentation Ak = 〈a, b | prod(a, b; k) = prod(b, a; k)〉 where prod(s, t; k) = ststs..., with k terms in the product on the right-hand side. We prove that the spherical growth series and the geodesic growth series of Ak with respect to the Artin generators {a, b, a, b−1} are rational. We provide explicit formulas for the series.
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