Relative symmetric polynomials and money change problem

2010/12/14 by M. Shahryari, Shahryari, Mohammad · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1012.2987

Abstract

This article is devoted to the number of non-negative solutions of the linear Diophantine equation a₁t₁+a₂t₂+... a_nt_n=d, where a₁, ..., 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.

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• Orthogonal bases of Brauer relative symmetric polynomials for certain groups

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