BG-ranks and 2-cores
William Y. C. Chen, Kathy Q. Ji, and Herbert S. Wilf
Abstract: We find the number of partitions of n whose BG-rank is j, in terms of pp(n), the
number of pairs of partitions whose total number of cells is n, giving both bijective
and generating function proofs. Next we find congruences mod 5 for pp(n), and then
we use these to give a new proof of a refined system of congruences for p(n) that was
found by Berkovich and Garvan.