The q-log-convexity of the Narayana polynomials of type B
نویسندگان
چکیده
منابع مشابه
The q-Log-convexity of the Narayana Polynomials of Type B
We prove a conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials of type B. By using Pieri’s rule and the JacobiTrudi identity for Schur functions, we obtain an expansion of a sum of products of elementary symmetric functions in terms of Schur functions with nonnegative coefficients. By the principal specialization this, leads to q-logconvexity. We also show that the lin...
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چکیده ندارد.
Schur positivity and the q-log-convexity of the Narayana polynomials
We prove two recent conjectures of Liu and Wang by establishing the strong q-log-convexity of the Narayana polynomials, and showing that the Narayana transformation preserves log-convexity. We begin with a formula of Brändén expressing the q-Narayana numbers as a specialization of Schur functions and, by deriving several symmetric function identities, we obtain the necessary Schur-positivity re...
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In this paper, we give a sufficient condition for the linear transformation preserving the strong q-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong q-log-convexity. In addition, our results not only extend some known results, but also imply the str...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2010
ISSN: 0196-8858
DOI: 10.1016/j.aam.2009.03.004