Partition identities and the coin exchange problem

摘要

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. (C) 2008 Elsevier Inc. All rights reserved.