Optimal transport and integer partitions

We link the theory of optimal transportation to the theory of integer partitions. Let P(n) denote the set of integer partitions of n∈N and write partitions π∈P(n) as (n1,…,nk(π)). Using terminology from optimal transport, we characterize certain classes of partitions like symmetric partitions and those in Euler's identity|{π∈P(n)∣all  ni  distinct}|=|{π∈P(n)∣all  ni  odd}|. Then we sketch how optimal transport might help to understand higher dimensional partitions.