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Algebra Discrete Math., 2018, Volume 26, Issue 1, Pages 1–7 (Mi adm665)  

RESEARCH ARTICLE

Unimodality polynomials and generalized Pascal triangles

Moussa Ahmiaa, Hacène Belbachirb

a University of Mohamed Seddik Ben Yahia, Department of Mathematics, RECITS Laboratory, BP 32, El Alia, 16111, Bab Ezzouar, Algiers, Algeria
b University of Sciences and Technology Houari Boumediene, Faculty of Mathematics, RECITS Laboratory, BP 32, El Alia, 16111, Bab Ezzouar, Algiers, Algeria

Abstract: In this paper, we show that if $P(x)=\sum_{k=0}^{m}a_{k}x^{k}$ is a polynomial with nondecreasing, nonnegative coefficients, then the coefficients sequence of $P(x^{s}+\cdots +x+1)$ is unimodal for each integer $s\geq 1$. This paper is an extension of Boros and Moll's result “A criterion for unimodality”, who proved that the polynomial $P(x+1)$ is unimodal.

Keywords: unimodality, log-concavity, ordinary multinomials, Pascal triangle.

Full text: PDF file (313 kB)
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MSC: 15A04, 11B65, 05A19, 52A37
Received: 04.04.2016
Revised: 18.05.2016
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Citation: Moussa Ahmia, Hacène Belbachir, “Unimodality polynomials and generalized Pascal triangles”, Algebra Discrete Math., 26:1 (2018), 1–7

Citation in format AMSBIB
\Bibitem{AhmBel18}
\by Moussa~Ahmia, Hac\`ene~Belbachir
\paper Unimodality polynomials and generalized Pascal triangles
\jour Algebra Discrete Math.
\yr 2018
\vol 26
\issue 1
\pages 1--7
\mathnet{http://mi.mathnet.ru/adm665}


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