Paul Hammond, Richard Lewis, "Congruences in ordered pairs of partitions", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 862780, 4 pages, 2004. https://doi.org/10.1155/S0161171204311439
Congruences in ordered pairs of partitions
Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence . 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 .
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