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Congruences in ordered pairs of partitions

By Paul Hammond and Richard Lewis

Abstract

Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a “birank” is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence\ud in p−2(n

Topics: QA101
Publisher: Hindawi Publishing Corporation
Year: 2004
OAI identifier: oai:sro.sussex.ac.uk:42663

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Citations

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