Strict unimodality of <i>q</i>-binomial coefficients

Pak, Igor; Panova, Greta

doi:10.1016/j.crma.2013.06.008

Combinatorics

Strict unimodality of q-binomial coefficients
[Lʼunimodalité stricte des coefficients q-binomiaux]

Présenté par : the Editorial Board

Pak, Igor ¹ ; Panova, Greta ¹

¹ Department of Mathematics, UCLA, Los Angeles, CA 90095, USA

Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 415-418.

Résumé
Abstract

Nous prouvons lʼunimodalité stricte des coefficients q-binomiaux ${(\begin{matrix} n \\ k \end{matrix})}_{q}$ comme polynômes en q. La preuve est basée sur la combinatoire de certains tableaux de Young et la propriété du semi-groupe des coefficients de Kronecker des représentations de $S_{n}$ .

We prove the strict unimodality of the q-binomial coefficients ${(\begin{matrix} n \\ k \end{matrix})}_{q}$ as polynomials in q. The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of $S_{n}$ representations.

Reçu le : 2013-04-24
Accepté le : 2013-06-24
Publié le : 2013-06-01

DOI : 10.1016/j.crma.2013.06.008

Affiliations des auteurs :

Pak, Igor ¹ ; Panova, Greta ¹

¹ Department of Mathematics, UCLA, Los Angeles, CA 90095, USA

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     title = {Strict unimodality of \protect\emph{q}-binomial coefficients},
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Pak, Igor; Panova, Greta. Strict unimodality of q-binomial coefficients. Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 415-418. doi : 10.1016/j.crma.2013.06.008. http://www.numdam.org/articles/10.1016/j.crma.2013.06.008/

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