The q-log-convexity of the Narayana polynomials of type B
The q-log-convexity of the Narayana polynomials of type B
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DOI：
10.1016/j.aam.2009.03.004
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
William Y. C. Chen;Robert L. Tang;Larry X. W. Wang;A. Yang
中科院分区：
文献类型：
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作者：
William Y. C. Chen;Robert L. Tang;Larry X. W. Wang;A. Yang
证明了刘和王关于B型Narayana多项式的q-对数凸性的一个猜想。利用Pieri法则和Schur函数的Jacobi-Trudi恒等式，我们得到了初等对称函数乘积之和关于非负系数Schur函数的展开式。通过主特殊化，这导致了q-对数凸性。我们还证明了关于B类Narayana数的三角阵列的线性变换是保持对数凸性的。
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 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. By the principal specialization, this leads to q-log-convexity. We also show that the linear transformation with respect to the triangular array of Narayana numbers of type B is log-convexity preserving.