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| HAL : inria-00622853, version 1 |
| arXiv : 1109.2688 |
| DOI : 10.1016/j.jcta.2012.05.007 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Journal of Combinatorial Theory, Series A 119, 8 (2012) 1711-1773 |
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| Algorithms for combinatorial structures: Well-founded systems and Newton iterations. |
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| Carine Pivoteau 1Bruno Salvy 2 |
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| (01/11/2012) |
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| We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet and Sedgewick with Joyal's species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative Newton method is shown to solve well-founded systems combinatorially. From there, truncations of the corresponding generating series are obtained in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. These results provide important subroutines in random generation. Finally, the approach is extended to combinatorial differential systems. |
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| 1 : | Laboratoire d'Informatique Gaspard-Monge (LIGM) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 |
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| 2 : | ARIC (Inria Grenoble Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme) |
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INRIA – CNRS : UMR5668 – Université Claude Bernard - Lyon I – École Normale Supérieure - Lyon |
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| 3 : | Laboratoire d'Informatique de Paris 6 (LIP6) |
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CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| Algo Algorithms APR |
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| Domaine | : | Mathématiques/Combinatoire |
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| Species theory – analytic combinatorics – generating series – complexity. |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00622853, version 1 | |
| http://hal.inria.fr/inria-00622853 | |
| oai:hal.inria.fr:inria-00622853 | |
| Contributeur : Bruno Salvy | |
| Soumis le : Lundi 12 Septembre 2011, 18:26:34 | |
| Dernière modification le : Lundi 17 Décembre 2012, 11:10:01 | |
