Enumeration of multi-colored rooted maps |
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Authors: | Didier Arquè s,Anne Micheli |
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Affiliation: | Équipe de synthèse d'images, Institut Gaspard Monge, Unité CNRS UPRES-A 8049, Université de Marne la Vallée, 5 Boulevard Descartes, Champs sur Marne, 77454 Marne la Vallée Cedex 2, France |
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Abstract: | We present a study of n-colored rooted maps in orientable and locally orientable surfaces. As far as we know, no work on these maps has yet been published. We give a system of n functional equations satisfied by n-colored orientable rooted maps regardless of genus and with respect to edges and vertices. We exhibit the solution of this system as a vector where each component has a continued fraction form and we deduce a new equation generalizing the Dyck equation for rooted planar trees. Similar results are shown for n-colored rooted maps in locally orientable surfaces. |
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Keywords: | Colored map Enumeration Generalized Dyck equation Multi-continued fraction |
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