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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| Дата: | 2018 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1932018-10-20T08:02:25Z Unimodality polynomials and generalized Pascal triangles Ahmia, Moussa Belbachir, Hacène unimodality, log-concavity, ordinary multinomials, Pascal triangle 15A04, 11B65, 05A19, 52A37 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. Lugansk National Taras Shevchenko University 2018-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193 Algebra and Discrete Mathematics; Vol 26, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/193/70 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/193/78 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/193/79 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
unimodality log-concavity ordinary multinomials Pascal triangle 15A04 11B65 05A19 52A37 |
| spellingShingle |
unimodality log-concavity ordinary multinomials Pascal triangle 15A04 11B65 05A19 52A37 Ahmia, Moussa Belbachir, Hacène Unimodality polynomials and generalized Pascal triangles |
| topic_facet |
unimodality log-concavity ordinary multinomials Pascal triangle 15A04 11B65 05A19 52A37 |
| format |
Article |
| author |
Ahmia, Moussa Belbachir, Hacène |
| author_facet |
Ahmia, Moussa Belbachir, Hacène |
| author_sort |
Ahmia, Moussa |
| title |
Unimodality polynomials and generalized Pascal triangles |
| title_short |
Unimodality polynomials and generalized Pascal triangles |
| title_full |
Unimodality polynomials and generalized Pascal triangles |
| title_fullStr |
Unimodality polynomials and generalized Pascal triangles |
| title_full_unstemmed |
Unimodality polynomials and generalized Pascal triangles |
| title_sort |
unimodality polynomials and generalized pascal triangles |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193 |
| work_keys_str_mv |
AT ahmiamoussa unimodalitypolynomialsandgeneralizedpascaltriangles AT belbachirhacene unimodalitypolynomialsandgeneralizedpascaltriangles |
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2024-04-12T06:27:24Z |
| last_indexed |
2024-04-12T06:27:24Z |
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1796109247335890944 |