Minimal and maximal elements in two-sided cells of Sn and Robinson-Schensted correspondence

Hohlweg, Christophe (2005). « Minimal and maximal elements in two-sided cells of Sn and Robinson-Schensted correspondence ». Discrete Mathematics, 304(1-3), pp. 79-87.

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Résumé

In symmetric groups, a two-sided cell is the set of all permutations which are mapped by the Robinson-Schensted correspondence on a pair of tableaux of the same shape. In this article, we show that the set of permutations in a two-sided cell which have a minimal number of inversions is the set of permutations which have a maximal number of inversions in conjugated Young subgroups. We also give an interpretation of these sets with particular tableaux, called reading tableaux. As corollary, we give the set of elements in a two-sided cell which have a maximal number of inversions.

Type: Article de revue scientifique
Mots-clés ou Sujets: Robinson-Schensted correspondence, number of inversions, twosided cells
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Christophe Hohlweg
Date de dépôt: 15 févr. 2016 14:58
Dernière modification: 20 avr. 2016 19:34
Adresse URL : http://www.archipel.uqam.ca/id/eprint/7817

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