STRICT UNIMODALITY OF q-BINOMIAL COEFFICIENTS
نویسندگان
چکیده
We prove strict unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of Sn representations. Résumé. Nous prouvons l’unimodalité stricte des coefficients q-binomiaux ( n k ) q comme des polynômes en q. La preuve est basée sur la combinatoire de certains Tableaux de Young et la propriété semi-groupe des coefficients Kronecker de Sn représentations. Introduction A sequence (a1, a2, . . . , an) is called unimodal, if for some k we have a1 ≤ a2 ≤ . . . ≤ ak ≥ ak+1 ≥ . . . ≥ an . The q-binomial (Gaussian) coefficients are defined as: ( m+ l m ) q = (qm+1 − 1) · · · (qm+l − 1) (q − 1) · · · (ql − 1) = lm ∑
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تاریخ انتشار 2013