BG-ranks and 2-cores

Details BG-ranks and 2-cores BG-ranks and 2-cores

2006-05-17

arxiv.org/abs/math/0605474v2

Mathematics

Combinatorics

Scientific paper

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.

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