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| HAL : hal-00018000, version 1 |
| arXiv : math.CO/0601678 |
| Fiche détaillée |  Récupérer au format |
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| Annals of Combinatorics 12, 1 (2008) 17-44 |
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| On triangulations with high vertex degree |
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| Olivier Bernardi 1 |
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| (2008) |
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| We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all vertices have degree at least d, for a certain value d chosen in {3, 4, 5}. The originality of the problem lies in the fact that degree restrictions are placed both on vertices and faces. Our proofs first follow Tutte's classical approach: we decompose maps by deleting the root and translate the decomposition into an equation satisfied by the generating function of the maps under consideration. Then we proceed to solve the equation obtained using a recent technique that extends the so-called quadratic method. |
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| 1 : | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
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CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunications de Bordeaux – Université Victor Segalen - Bordeaux II |
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| Domaine | : | Mathématiques/Combinatoire |
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| planar map – triangulation – generating function – catalytic variable – asymptotic enumeration |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00018000, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00018000 | |
| oai:hal.archives-ouvertes.fr:hal-00018000 | |
| Contributeur : Olivier Bernardi | |
| Soumis le : Vendredi 27 Janvier 2006, 15:48:38 | |
| Dernière modification le : Jeudi 18 Juin 2009, 14:05:52 | |
