Partition identities and the coin exchange problem

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 and 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.

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: Alexander E. Holroyd
• Keywords: Analogous Identities, Identities, JCT 2008, Non-negative Integer Combination