  A result of Hohloch links the theory of integer partitions with the Monge
formulation of the optimal transport problem, giving the optimal transport map
between (Young diagrams of) integer partitions and their corresponding
symmetric partitions. Our aim is to extend Hohloch's result to the higher
dimensional case. In doing so, we show the Kantorovich formulation of the
optimal transport problem provides the tool to study the matching of higher
dimensional partitions with their corresponding symmetric partitions.
