Geodesic
Ratio monotonicity of polynomials derived from nondecreasing sequences
The electronic journal of combinatorics, Tome 17 (2010)
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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 $c\geq 1$ due to Llamas and Martínez-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.
DOI : 10.37236/486
Classification : 05A20, 33F10
Mots-clés : log-concavity, ratio monotonicity, Boros-Moll polynomials 
@article{10_37236_486,
     author = {William Y. C. Chen and Arthur L. B. Yang and Elaine L. F. Zhou},
     title = {Ratio monotonicity of polynomials derived from nondecreasing sequences},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/486},
     zbl = {1204.05025},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/486/}
}
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William Y. C. Chen; Arthur L. B. Yang; Elaine L. F. Zhou. Ratio monotonicity of polynomials derived from nondecreasing sequences. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/486

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