Unimodality polynomials and generalized Pascal triangles
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...
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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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