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...
Збережено в:
| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1162 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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