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Dyson's Partition Ranks and their Multiplicative Extensions (1607.03846v1)
Published 13 Jul 2016 in math.NT
Abstract: We study the Dyson rank function $N(r,3;n)$, the number of partitions of $n$ with rank $\equiv r \pmod 3$. We investigate the convexity of these functions. We extend $N(r,3;n)$ multiplicatively to the set of partitions, and we determine the maximum value when taken over all partitions of size $n$.
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