Experiments on growth series of braid groups

Jean Fromentin (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We introduce an algorithmic framework to investigate spherical and geodesic growth series of braid groups relatively to the Artin's or Birman-Ko-Lee's generators. We present our experimentations in the case of three and four strands and conjecture rational expressions for the spherical growth series with respect to the Birman-Ko-Lee's generators.

Mots clés: Braid group; spherical growth series; geodesic growth series; algorithm

Domaines: Théorie des groupes [math.GR]; Combinatoire [math.CO]

Jean Fromentin. Experiments on growth series of braid groups. 2021. ⟨hal-02929264v3⟩