Geodesic
Relative symmetric polynomials and money change problem
Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 287-292.

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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.
Keywords: Money change problem; Partitions of integers; Relative symmetric polynomials; Symmetric groups; Complex characters. 
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M. Shahryari. Relative symmetric polynomials and money change problem. Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 287-292. http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a9/

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