Log-convexity and strong q-log-convexity for some triangular arrays |
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Authors: | Bao-Xuan Zhu |
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Affiliation: | School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, PR China |
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Abstract: | We give a criterion for the log-convexity (resp. the strong q -log-convexity) of the first column of certain infinite triangular array (An,k)0?k?n of nonnegative numbers (resp. of polynomials in q with nonnegative coefficients), for which the recurrence relation is of the form This allows a unified treatment of the log-convexity of the Catalan-like numbers, as well as that of the q-log-convexity of some classical polynomials. In particular, we obtain simple proofs of the q-log-convexity of Narayana polynomials. |
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Keywords: | 05A20 15A15 |
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