The infinite-state Potts model and restricted multidimensional partitions of an integer

It is shown that the partition function of the q-state Potts model on a finite d-dimensional hypercubic lattice in the q --> infinity limit is precisely the generating function of (d-1)-dimensional restricted partitions of an integer. For d = 2, 3, this equivalence leads to closed-form expressions of the q = infinity Potts partition function. Our discussion also establishes symmetry and reciprocal properties for the generating function of restricted partitions in higher dimensions.