The q-Log-convexity of the Generating Functions of the Squares of Binomial Coefficients

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dc.creatorChen, William Y. C.
dc.creatorTang, Robert L.
dc.creatorWang, Larry X. W.
dc.creatorYang, Arthur L. B.
dc.date2008-10-13
dc.date.accessioned2026-07-07T10:09:38Z
dc.date.available2026-07-07T10:09:38Z
dc.descriptionWe prove a conjecture of Liu and Wang on the q-log-convexity of the polynomial sequence $\{\sum_{k=0}^n{n\choose k}^2q^k\}_{n\geq 0}$. By using Pieri's rule and the Jacobi-Trudi 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. Then the principal specialization leads to the q-log-convexity. We also prove that a technical condition of Liu and Wang holds for the squares of the binomial coefficients. Hence we deduce that the linear transformation with respect to the triangular array $\{{n\choose k}^2\}_{0\leq k\leq n}$ is log-convexity preserving.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/0810.2247
dc.identifierhttp://arxiv.org/abs/0810.2247
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171378
dc.subjectCombinatorics
dc.titleThe q-Log-convexity of the Generating Functions of the Squares of Binomial Coefficients
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