Unimodality polynomials and generalized Pascal triangles

• Date: 2018
• Main Authors: Ahmia, Moussa, Belbachir, Hacène
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: unimodality; log-concavity; ordinary multinomials; Pascal triangle; 15A04; 11B65; 05A19; 52A37
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193
• Journal Title: Algebra and Discrete Mathematics

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...