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 ( n 1 , � , n k ( 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� n i �distinct } | = | { π � P ( n ) � all� n i �odd } | . Then we sketch how optimal transport might help to understand higher dimensional partitions.