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| HAL : hal-00418457, version 1 |
| arXiv : 0904.4854 |
| DOI : 10.1016/j.ejc.2011.09.035 |
| Fiche détaillée |  Récupérer au format |
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| European Journal of Combinatorics 33 (2012) 189-198 |
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| Partial Jucys-Murphy elements and star factorizations |
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| Valentin Féray 1 |
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| (01/02/2012) |
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| In this paper, we look at the number of factorizations of a given permutation into star transpositions. In particular, we give a natural explanation of a hidden symmetry, answering a question of I.P. Goulden and D.M. Jackson. We also have a new proof of their explicit formula. Another result is the normalized class expansion of some central elements of the symmetric group algebra introduced by P. Biane. To obtain this results, we use natural analogs of Jucys-Murphy elements in the algebra of partial permutations of V. Ivanov and S. Kerov. We investigate their properties and use a formula of A. Lascoux and J.Y. Thibon to give the expansion of their power sums on the natural basis of the invariant subalgebra. |
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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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| Domaine | : | Mathématiques/Combinatoire |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/0904.4854 |
| hal-00418457, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00418457 | |
| oai:hal.archives-ouvertes.fr:hal-00418457 | |
| Contributeur : Valentin Feray | |
| Soumis le : Vendredi 18 Septembre 2009, 16:07:24 | |
| Dernière modification le : Lundi 2 Juillet 2012, 10:48:07 | |
