Une relation fonctionnelle nouvelle sur les cartes planaires pointées (Q1061742)

A new functional relation, the unique solution of which is the generating function of rooted planar maps, is shown. This new relation in conjunction with the well-known relation established by Tutte, enables the easy derivation of a system of parametric equations for the desired generating function. As a consequence, one infers a closed formula counting the rooted planar maps as a function of their number of vertices and faces. The geometrical nature of the decomposition used in the derivation of this functional relation leads to the definition of a natural notion of the inner map of a rooted planar map. Some questions related to this notion are treated.