Congruences in ordered pairs of partitions
Summary: 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 \(p_{-2}(n)\).
scientific article; zbMATH DE number 2171612
scientific article