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| HAL : hal-00068433, version 1 |
| arXiv : math.CO/0605320 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Combinatorial Theory Series A 114, 5 (2007) 931-956 |
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| Bijective counting of Kreweras walks and loopless triangulations |
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| Olivier Bernardi 1 |
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| (2007) |
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| We consider lattice walks in the plane starting at the origin, remaining in the first quadrant and made of West, South and North-East steps. In 1965, Germain Kreweras discovered a remarkably simple formula giving the number of these walks (with prescribed length and endpoint). Kreweras' proof was very involved and several alternative derivations have been proposed since then. But the elegant simplicity of the counting formula remained unexplained. We give the first purely combinatorial explanation of this formula. Our approach is based on a bijection between Kreweras walks and triangulations with a distinguished spanning tree. We obtain simultaneously a bijective way of counting loopless triangulations. |
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| 1 : | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
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CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II |
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| Domaine | : | Mathématiques/Combinatoire |
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| planar walk – Kreweras walk – planar map – triangulation – cubic map – bijection – counting – DFS |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00068433, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00068433 | |
| oai:hal.archives-ouvertes.fr:hal-00068433 | |
| Contributeur : Olivier Bernardi | |
| Soumis le : Jeudi 11 Mai 2006, 19:58:29 | |
| Dernière modification le : Jeudi 18 Juin 2009, 14:06:51 | |
