Relative symmetric polynomials and money change problem
This article is devoted to the number of non-negative solutions of the linear Diophantine equation\[a_1t_1+a_2t_2+\cdots +a_nt_n=d,\]where \(a_1, \ldots, a_n\), and \(d\) are positive integers. We obtain a relation between the number of solutions of this equation and characters of the symmetric gro...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1162 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-11622018-05-16T05:04:06Z Relative symmetric polynomials and money change problem Shahryari, M. Money change problem; Partitions of integers; Relative symmetric polynomials; Symmetric groups; Complex characters Primary 05A17, Secondary 05E05 and 15A69 This article is devoted to the number of non-negative solutions of the linear Diophantine equation\[a_1t_1+a_2t_2+\cdots +a_nt_n=d,\]where \(a_1, \ldots, a_n\), and \(d\) are positive integers. We obtain a relation between the number of solutions of this equation and characters of the symmetric group, using relative symmetric polynomials. As an application, we give a necessary and sufficient condition for the space of the relative symmetric polynomials to be non-zero. Lugansk National Taras Shevchenko University 2018-05-16 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1162 Algebra and Discrete Mathematics; Vol 16, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1162/654 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-05-16T05:04:06Z |
| collection |
OJS |
| language |
English |
| topic |
Money change problem Partitions of integers Relative symmetric polynomials Symmetric groups Complex characters Primary 05A17 Secondary 05E05 and 15A69 |
| spellingShingle |
Money change problem Partitions of integers Relative symmetric polynomials Symmetric groups Complex characters Primary 05A17 Secondary 05E05 and 15A69 Shahryari, M. Relative symmetric polynomials and money change problem |
| topic_facet |
Money change problem Partitions of integers Relative symmetric polynomials Symmetric groups Complex characters Primary 05A17 Secondary 05E05 and 15A69 |
| format |
Article |
| author |
Shahryari, M. |
| author_facet |
Shahryari, M. |
| author_sort |
Shahryari, M. |
| title |
Relative symmetric polynomials and money change problem |
| title_short |
Relative symmetric polynomials and money change problem |
| title_full |
Relative symmetric polynomials and money change problem |
| title_fullStr |
Relative symmetric polynomials and money change problem |
| title_full_unstemmed |
Relative symmetric polynomials and money change problem |
| title_sort |
relative symmetric polynomials and money change problem |
| description |
This article is devoted to the number of non-negative solutions of the linear Diophantine equation\[a_1t_1+a_2t_2+\cdots +a_nt_n=d,\]where \(a_1, \ldots, a_n\), and \(d\) are positive integers. We obtain a relation between the number of solutions of this equation and characters of the symmetric group, using relative symmetric polynomials. As an application, we give a necessary and sufficient condition for the space of the relative symmetric polynomials to be non-zero. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1162 |
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AT shahryarim relativesymmetricpolynomialsandmoneychangeproblem |
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2025-07-17T10:30:54Z |
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2025-07-17T10:30:54Z |
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1837890131160203264 |