Partition Identities and the Coin Exchange Problem
Combinatorics
2007-06-18 v1 Number Theory
Abstract
The number of partitions of n into parts divisible by a or b equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of a or b. This generalizes identities of MacMahon and Andrews. The analogous identities for three or more integers (in place of a,b) hold in certain cases.
Cite
@article{arxiv.0706.2282,
title = {Partition Identities and the Coin Exchange Problem},
author = {Alexander E. Holroyd},
journal= {arXiv preprint arXiv:0706.2282},
year = {2007}
}