Zeilberger’s KOH theorem and the strict unimodality of $q$-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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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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Abstract. The q-binomial coefficient is a polynomial in q. Given an integer t and a residue class r modulo t, a sieved q-binomial coefficient is the sum of those terms whose exponents are congruent to r modulo t. In this paper explicit polynomial identities in q are given for sieved q-binomial coefficients. As a limiting case, generating functions for the sieved partition function are found as ...
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We present a lower bound on the Kronecker coefficients of the symmetric group via the characters of Sn, which we apply to obtain various explicit estimates. Notably, we extend Sylvester’s unimodality of q-binomial coefficients ( n k ) q as polynomials in q to derive sharp bounds on the differences of their consecutive coefficients.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2015-12510-5