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Une relation fonctionnelle nouvelle sur les cartes planaires pointées. (French) Zbl 0571.05001

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.
Reviewer: Ph.Vincke

MSC:

05A15 Exact enumeration problems, generating functions
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:

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