Geodesic
BG-ranks and 2-cores
The electronic journal of combinatorics, Tome 13 (2006)
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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.
DOI : 10.37236/1156
Classification : 05A17, 11P81, 11P83
Mots-clés : number of partitions, generating function 
@article{10_37236_1156,
     author = {William Y. C. Chen and Kathy Q. Ji and Herbert S. Wilf},
     title = {BG-ranks and 2-cores},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1156},
     zbl = {1111.05007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1156/}
}
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William Y. C. Chen; Kathy Q. Ji; Herbert S. Wilf. BG-ranks and 2-cores. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1156

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