English

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.

Keywords

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}
}
R2 v1 2026-06-21T08:38:52.174Z