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Cylindric Partitions and Branes

We show that the generating function of the cylindric partitions is given by the open topological string partition function of a CY3-fold. Type IIA string theory compactified on this CY3-fold gives rise to N=2 U(1) gauge theory with an adjoint hypermultiplet. The two Kahler parameters of the geometry, which are quantized in units of the string coupling constant, and the representation of the branes are given by the profile of the cylindric partition. We relate the level-rank duality of the cylindric generating function to the exchange symmetry of the two Kahler parameters.