BG-ranks and 2-cores
Combinatorics
2007-05-23 v2
Abstract
We find the number of partitions of whose BG-rank is , in terms of , the number of pairs of partitions whose total number of cells is , giving both bijective and generating function proofs. Next we find congruences mod 5 for , and then we use these to give a new proof of a refined system of congruences for that was found by Berkovich and Garvan.
Cite
@article{arxiv.math/0605474,
title = {BG-ranks and 2-cores},
author = {William Y. C. Chen and Kathy Q. Ji and Herbert S. Wilf},
journal= {arXiv preprint arXiv:math/0605474},
year = {2007}
}