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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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543245792706560 |
|---|---|
| author | Ahmia, Moussa Belbachir, Hacène |
| author_facet | Ahmia, Moussa Belbachir, Hacène |
| author_sort | Ahmia, Moussa |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-10-20T08:02:25Z |
| 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. |
| first_indexed | 2025-12-02T15:30:38Z |
| format | Article |
| id | admjournalluguniveduua-article-193 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:38Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | unimodality log-concavity ordinary multinomials Pascal triangle 15A04 11B65 05A19 52A37 Ahmia, Moussa Belbachir, Hacène Unimodality polynomials and generalized Pascal triangles |
| title | 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_short | Unimodality polynomials and generalized Pascal triangles |
| title_sort | unimodality polynomials and generalized pascal triangles |
| topic | unimodality log-concavity ordinary multinomials Pascal triangle 15A04 11B65 05A19 52A37 |
| topic_facet | unimodality log-concavity ordinary multinomials Pascal triangle 15A04 11B65 05A19 52A37 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/193 |
| work_keys_str_mv | AT ahmiamoussa unimodalitypolynomialsandgeneralizedpascaltriangles AT belbachirhacene unimodalitypolynomialsandgeneralizedpascaltriangles |