Abstract
We show here, by using two distinct geometrical decompositions of rooted planar hypermaps, that there exists two functional relations whose unique solution is the generating function enumerating rooted planar hypermaps.
Used together, these two relations allow us to obtain, without any hard formal calculus, a really simple system of parametric equations for the generating series enumerating rooted planar hypermaps by their number of vertices, faces and hyperedges. From this we get the general term of this series.
One of the above cited geometrical decompositions leads us to define a natural notion of the inner hypermap of a rooted planar hypermap. Some enumerations related to this notion are treated.
Keywords
- Geometrical Decomposition
- Definition Utilisees
- Simplement Connexes
- Sont Identifiees
- Circuit Bordant
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Bibliographie
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© 1986 Springer-Verlag
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Arques, D. (1986). Relations fonctionnelles et denombrement des hypercartes planaires pointees. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072505
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DOI: https://doi.org/10.1007/BFb0072505
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