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| HAL : hal-00018111, version 1 |
| arXiv : math.CO/0601684 |
| Fiche détaillée |  Récupérer au format |
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| The Electronic Journal of Combinatorics 14 (2007) R9 |
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| Bijective counting of tree-rooted maps and shuffles of parenthesis systems |
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| Olivier Bernardi 1 |
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| (2007) |
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| The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long awaited) simple bijection which explains this result. We prove that our bijection is isomorphic to a former recursive construction on shuffles of parenthesis systems due to Cori, Dulucq and Viennot. |
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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 maps – tree-rooted maps – spanning tree – parethesis system – planar walks – bijection – enumeration |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00018111, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00018111 | |
| oai:hal.archives-ouvertes.fr:hal-00018111 | |
| Contributeur : Olivier Bernardi | |
| Soumis le : Vendredi 27 Janvier 2006, 18:51:13 | |
| Dernière modification le : Jeudi 18 Juin 2009, 14:06:20 | |
