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Congruences in ordered pairs of partitions

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  • Paul Hammond
  • 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 in p − 2 ( n ) .

Suggested Citation

  • Paul Hammond & Richard Lewis, 2004. "Congruences in ordered pairs of partitions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:862780
    DOI: 10.1155/S0161171204311439
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