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Article overview
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The q-Log-convexity of the Generating Functions of the Squares of Binomial Coefficients | | William Y. C. Chen
; Robert L. Tang
; Larry X. W. Wang
; Arthur L. B. Yang
; | | Date: |
13 Oct 2008 | | Abstract: | We prove a conjecture of Liu and Wang on the q-log-convexity of the
polynomial sequence ${sum_{k=0}^n{nchoose k}^2q^k}_{ngeq 0}$. 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 ${{nchoose k}^2}_{0leq kleq n}$ is log-convexity preserving. | | Source: | arXiv, 0810.2247 | | Services: | Forum | Review | PDF | Favorites | |
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