The q-log-convexity of the Narayana polynomials of type B

被引：37

作者：

Chen, William Y. C. ^{[1
]}

Tang, Robert L. ^{[1
]}

Wang, Larry X. W. ^{[1
]}

Yang, Arthur L. B. ^{[1
]}

机构：

[1] Nankai Univ, LPMC TJKLC, Ctr Combinator, Tianjin 300071, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS | 2010年 / 44卷 / 02期

基金：

美国国家科学基金会;

关键词：

q-log-convexity; Schur positivity; Pieri's rule; The Jacobi-Trudi identity; Principal specialization; Narayana numbers of type B; CONCAVITY;

D O I：

10.1016/j.aam.2009.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：85 / 110

页数：26

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