Title: Optimal transport and integer partitions,
Abstract: We link the theory of optimal transportation to the theory of integer
partitions. Let $\mathscr P(n)$ denote the set of integer partitions of $n \in
\mathbb N$ and write partitions $\pi \in \mathscr P(n)$ as $(n_1, \dots,
n_{k(\pi)})$. Using terminology from optimal transport, we characterize certain
classes of partitions like symmetric partitions and those in Euler's identity
$|\{ \pi \in \mathscr P(n) |$ all $ n_i $ distinct $ \} | = | \{ \pi \in
\mathscr P(n) | $ all $ n_i $ odd $ \}|$.
Then we sketch how optimal transport might help to understand higher
dimensional partitions.