The polynomial part of a restricted partition function related to the Frobenius problem

2003/06/02 by Matthias Beck, Ira M. Gessel, Takao Komatsu · 1 citation
Mathematics · #math.CO #math.NT #msc:05A15 #msc:11P81 #msc:05A17

paper · pdf

published as Electronic J. Comb. 8, no. 1 (2001), N 7 · 5 pages

arxiv created 2003/06/02 · arxiv updated 2009/11/30

Abstract

Given a set of positive integers A = a₁,...,a_n, we study the number p_A (t) of nonnegative integer solutions (m₁,...,m_n) to m₁ a₁ + ... m_n a_n = t. We derive an explicit formula for the polynomial part of p_A.

Cited by

• Counting with two-level polynomials

Related

• The generalized Frobenius problem via restricted partition functions
• On the restricted partition function II
• Refined upper bounds for the linear Diophantine problem of Frobenius
• Partitions of finite nonnegative integer sets with identical representation functions
• The parametric Frobenius problem and parametric exclusion