Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences
Combinatorics
2010-07-29 v1 Classical Analysis and ODEs
Abstract
The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x+1), which leads to the log-concavity of P(x+c) for any due to Llamas and Mart\'{\i}nez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Chen and Xia without resorting to the recurrence relations of the coefficients.
Cite
@article{arxiv.1007.5017,
title = {Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences},
author = {William Y. C. Chen and Arthur L. B. Yang and Elaine L. F. Zhou},
journal= {arXiv preprint arXiv:1007.5017},
year = {2010}
}
Comments
9 pages