Refined upper bounds for the linear Diophantine problem of Frobenius
Number Theory
2007-05-23 v2 Combinatorics
Abstract
We study the Frobenius problem: given relatively prime positive integers a_1,...,a_d, find the largest value of t (the Frobenius number g(a_1,...,a_d)) such that m_1 a_1 + ... m_d a_d = t has no solution in nonnegative integers m_1,...,m_d. We introduce a method to compute upper bounds for g(a_1,a_2,a_3), which seem to grow considerably slower than previously known bounds. Our computations are based on a formula for the restricted partition function, which involves Dedekind-Rademacher sums, and the reciprocity law for these sums.
Keywords
Cite
@article{arxiv.math/0305420,
title = {Refined upper bounds for the linear Diophantine problem of Frobenius},
author = {Matthias Beck and Shelemyahu Zacks},
journal= {arXiv preprint arXiv:math/0305420},
year = {2007}
}
Comments
12 pages, 5 figures