Article Dans Une Revue International Journal of Algebra and Computation Année : 2006

Growth series for Artin groups of dihedral type

Résumé

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, and inverses) are rational. We provide explicit formulas for the series.

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hal-00164813 , version 1 (23-07-2007)

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  • HAL Id : hal-00164813 , version 1

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Jean Mairesse, Frédéric Mathéus. Growth series for Artin groups of dihedral type. International Journal of Algebra and Computation, 2006, 16 (6), pp.1087-1107. ⟨hal-00164813⟩
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