This article is cited in 3 papers

RESEARCH ARTICLE

Relative symmetric polynomials and money change problem

M. Shahryari

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Abstract: 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.

MSC: Primary 05A17; Secondary 05E05,15A69

Received: 08.04.2012
Revised: 28.04.2012

Language: English

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