Chapoton, Frédéric

Sur une série en arbres à deux paramètres

Sémin. Lothar. Comb. 70, B70a, 20 p. (2013)


Summary: We define 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 $x = -1/q$, we recover the tree-indexed series $\Omega_{q}$ that was introduced in a previous article as a $q$-analog of a classical tree-indexed series $\Omega$.