no. 10
Combinatorics/Group theory
Combinatorics on a family of reduced Kronecker coefficients

Présenté par : Michèle Vergne

Colmenarejo, Laura1 ; Rosas, Mercedes1
1 Department of Algebra, University of Seville, Spain
Comptes Rendus. Mathématique, Tome 353 (2015) no. 10, pp. 865-869.

Les coefficients de Kronecker réduits sont des coefficients de Kronecker particuliers, qui permettent néanmoins de recalculer tous les coefficients de Kronecker. Dans cette note, nous calculons la fonction génératrice d'une famille particulière de coefficients de Kronecker réduits. Nous exprimons sa relation avec les partitions planes, ce qui nous permet de vérifier que cette famille possède la propriété de saturation, ainsi que la propriété de monotonie. Grâce à cette fonction génératrice, nous pouvons décrire les coefficients considérés au moyen d'une formule quasi polynomiale, dont nous précisons le degré et la période.

The reduced Kronecker coefficients are particular instances of Kronecker coefficients, that nevertheless contain enough information to compute all Kronecker coefficients from them. In this note, we compute the generating function of a family of reduced Kronecker coefficients. We show that these reduced Kronecker coefficients count plane partitions. This allows us to check that these coefficients satisfy the saturation conjecture, and that they are weakly increasing. Thanks to its generating function, we can describe our family by a quasipolynomial, specifying its degree and period.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.07.012
Colmenarejo, Laura 1 ; Rosas, Mercedes 1

1 Department of Algebra, University of Seville, Spain 
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Colmenarejo, Laura; Rosas, Mercedes. Combinatorics on a family of reduced Kronecker coefficients. Comptes Rendus. Mathématique, Tome 353 (2015) no. 10, pp. 865-869. doi : 10.1016/j.crma.2015.07.012. http://www.numdam.org/articles/10.1016/j.crma.2015.07.012/

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☆ Both authors are partially supported by MTM2013-40455-P, P12-FQM-2696, FQM-333, and FEDER.