Congruences in ordered pairs of partitions

Paul Hammond and Richard Lewis

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-4

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 in p − 2 ( n ) .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:862780

DOI: 10.1155/S0161171204311439

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