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| HAL: hal-00655531, version 1 |
| arXiv: 1112.6379 |
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| Constellations and multicontinued fractions: application to Eulerian triangulations |
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| Marie Albenque 1Jérémie Bouttier 2, 3 |
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| (2011-12-29) |
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| We consider the problem of enumerating planar constellations with two points at a prescribed distance. Our approach relies on a combinatorial correspondence between this family of constellations and the simpler family of rooted constellations, which we may formulate algebraically in terms of multicontinued fractions and generalized Hankel determinants. As an application, we provide a combinatorial derivation of the generating function of Eulerian triangulations with two points at a prescribed distance. |
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| 1: | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| 2: | Institut de Physique Théorique (ex SPhT) (IPHT) |
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CNRS : URA2306 – CEA : DSM/IPHT |
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| 3: | Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA) |
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CNRS : UMR7089 – Université Paris VII - Paris Diderot |
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| Subject | : | Mathematics/Combinatorics Physics/Mathematical Physics Mathematics/Mathematical Physics |
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| Constellations – planar maps – Eulerian triangulations – continued fractions – lattice paths |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1112.6379 |
| hal-00655531, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00655531 | |
| oai:hal.archives-ouvertes.fr:hal-00655531 | |
| From: Jérémie Bouttier | |
| Submitted on: Friday, 30 December 2011 10:43:48 | |
| Updated on: Thursday, 28 June 2012 08:49:19 | |
