posted on 2023-06-08, 13:47authored byPaul Hammond, Richard Lewis
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)
History
Publication status
Published
Journal
International Journal of Mathematics and Mathematical Sciences
The interested reader might also like to look at Frank Garvan's "Biranks for partitions into 2 colors" http://arxiv.org/pdf/0909.4892.pdf and http://www.math.ufl.edu/~fgarvan/papers/birank.pdf