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| HAL : hal-00164584, version 1 |
| arXiv : 0707.3185 |
| Fiche détaillée |  Récupérer au format |
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| International Journal of Algebra and Computation 18, 1 (2008) 375-405 |
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| Random generation of finitely generated subgroups of a free group |
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| Frédérique Bassino 1Cyril Nicaud 1 |
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| (2008) |
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| We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be obtained by the method of Stallings foldings. Our algorithm randomly generates a subgroup of a given size $n$, according to the uniform distribution over size $n$ subgroups. In the process, we give estimates of the number of size $n$ subgroups, of the average rank of size $n$ subgroups, and of the proportion of such subgroups that have finite index. Our algorithm has average case complexity $\O(n)$ in the RAM model and $\O(n^2\log^2n)$ in the bitcost model. |
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| 1 : | Laboratoire d'Informatique Gaspard-Monge (LIGM) |
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Université Paris Est Marne-la-Vallée – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 |
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| 2 : | 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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| Méthodes Formelles |
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| Domaine | : | Mathématiques/Théorie des groupes Mathématiques/Combinatoire |
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| subgroups of free groups – random generation |
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| hal-00164584, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00164584 | |
| oai:hal.archives-ouvertes.fr:hal-00164584 | |
| Contributeur : Pascal Weil | |
| Soumis le : Vendredi 20 Juillet 2007, 19:30:15 | |
| Dernière modification le : Mardi 27 Décembre 2011, 10:59:44 | |
