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arXiv · 1607.03846

Dyson's Partition Ranks and their Multiplicative Extensions

Elaine Hou·Meena Jagadeesan
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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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Elaine Hou, Meena Jagadeesan. 2016-07-13. Dyson's Partition Ranks and their Multiplicative Extensions. https://arxiv.org/abs/1607.03846

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