# Partition identities and the coin exchange problem

@article{Holroyd2008PartitionIA, title={Partition identities and the coin exchange problem}, author={Alexander E. Holroyd}, journal={J. Comb. Theory, Ser. A}, year={2008}, volume={115}, pages={1096-1101} }

- Published 2008 in J. Comb. Theory, Ser. A
DOI:10.1016/j.jcta.2007.12.003

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.

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