Sur une série en arbres à deux paramètres

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

One defines a new tree-indexed series, with coefficients that are polynomials in x over the ring Q(q). Several special evaluations of this series are obtained, in particular when x is replaced by a q-integer. By taking a limit value when x = -1/q, one recovers the tree-indexed series Omega_q that was introduced in a previous article as a q-analog of a classical tree-indexed series Omega.

Mots clés: rooted tree; prelie algebra; increasing coloring; q-integer

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. Sur une série en arbres à deux paramètres. Seminaire Lotharingien de Combinatoire, 2013, 70, pp.n/a. ⟨hal-00771659⟩