Dyson's Partition Ranks and their Multiplicative Extensions
  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 $n$. 
Elaine Hou and Meena Jagadeesan
math.NT