Geodesic
Partition statistics for cubic partition pairs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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In this brief note, we give two partition statistics which explain the following partition congruences: \begin{align*} b(5n+4) &\equiv 0 \pmod{5}, \\ b(7n+a) &\equiv 0 \pmod{7}, \text{if $a=2$, $3$, $4$, or $6$}. \end{align*} Here, $b(n)$ is the number of $4$-color partitions of $n$ with colors $r$, $y$, $o$, and $b$ subject to the restriction that the colors $o$ and $b$ appear only in even parts.
DOI : 10.37236/615
Classification : 05A17, 11P83 
@article{10_37236_615,
     author = {Byungchan Kim},
     title = {Partition statistics for cubic partition pairs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/615},
     zbl = {1238.05018},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/615/}
}
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Byungchan Kim. Partition statistics for cubic partition pairs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/615

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