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BG-ranks and 2-cores

William Y. C. Chen·Kathy Q. Ji·Herbert S. Wilf
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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.

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William Y. C. Chen, Kathy Q. Ji, Herbert S. Wilf. 2006-05-17. BG-ranks and 2-cores. https://arxiv.org/abs/math/0605474

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