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arXiv · 1008.0310

Interlacing Log-concavity of the Boros-Moll Polynomials

William Y. C. Chen·Larry X. W. Wang·Ernest X. W. Xia
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Abstract

We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.

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William Y. C. Chen, Larry X. W. Wang, Ernest X. W. Xia. 2010-08-02. Interlacing Log-concavity of the Boros-Moll Polynomials. https://arxiv.org/abs/1008.0310

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