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

Optimal transport for some symmetric, multidimensional integer partitions