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arXiv · 1903.05857

Asymptotic equidistribution and convexity for partition ranks

Joshua Males
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Abstract

We study the Dyson rank function $N(r,t;n)$, the number of partitions with rank congruent to $r$ modulo $t$. We first show that it is monotonic in $n$, and then show that it equidistributed as $n \rightarrow \infty$. Using this result we prove a conjecture of Hou and Jagadeeson on the convexity of $N(r,t;n)$.

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Joshua Males. 2019-08-02. Asymptotic equidistribution and convexity for partition ranks. https://doi.org/10.1007/s11139-019-00202-8

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