A combinatorial proof of strict unimodality for q-binomial coefficients
نویسندگان
چکیده
منابع مشابه
STRICT UNIMODALITY OF q-BINOMIAL COEFFICIENTS
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 Tabl...
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q-binomial coefficient identity Victor J. W. Guo and Jiang Zeng Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China [email protected], http://math.ecnu.edu.cn/~jwguo Université de Lyon; Université Lyon 1; Institut Camille Jordan, UMR 5208 du CNRS; 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France [email protected], ...
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This paper is devoted to the study of certain unimodal sequences related to binomial coefficients. Although the paramount purpose is to prove unimodality, in a few cases we even determine the maxima of the sequences. Our new results generalize some earlier theorems on unimodality. The proof techniques are quite varied. This research is supported by the János Bolyai Scholarship of HAS, and by th...
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In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations. The construction and derivation of these result...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.07.001