Geodesic
Unimodality polynomials and generalized Pascal triangles
Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 1-7

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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
Mots-clés : Pascal triangle. 
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     author = {Moussa Ahmia and Hac\`ene Belbachir},
     title = {Unimodality polynomials and generalized {Pascal} triangles},
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Moussa Ahmia; Hacène Belbachir. Unimodality polynomials and generalized Pascal triangles. Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 1-7. http://geodesic.mathdoc.fr/item/ADM_2018_26_1_a1/