Korean J. Math.  Vol 23, No 4 (2015)  pp.637-642
DOI: https://doi.org/10.11568/kjm.2015.23.4.637

Cubic partition pairs weighted by the parity of the crank

Byungchan Kim

Abstract


We study congruence properties of the number of cubic partition pairs weighted by the parity of the crank. If we define such number to be $c(n)$, then
\[
c(5n+4) \equiv 0 \pmod{5} \;\; \text{ and } \;\; c(7n+2) \equiv 0 \pmod{7},
\]
for all nonnegative integers $n$.


Keywords


Partitions, Partition crank, cubic partitions, cubic crank, congruences

Subject classification

11P82

Sponsor(s)

This study was supported by the Research Program funded by the Seoul National University of Science and Technology.

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