相对对称多项式与货币兑换问题
Relative symmetric polynomials and money change problem
摘要：
本文研究了线性丢番图方程$$ a_1t_1+a_2t_2+... a_nt_n=d, $$的非负解的个数，其中$a_1, ..., a_n$，和$d$是正整数.利用{ \em相对对称多项式}得到了该方程的解的个数与对称群特征的关系。作为应用，我们给出了相对对称多项式空间非零的一个充要条件。
英文摘要：
This article is devoted to the number of non-negative solutions of the linear Diophantine equation $$ a_1t_1+a_2t_2+... a_nt_n=d, $$ where $a_1, ..., a_n$, and $d$ are positive integers. We obtain a relation between the number of solutions of this equation and characters of the symmetric group, using {\em 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
