  Type IIA string theory compactified on an elliptic CY3-fold gives rise to N=2
U(1) gauge theory with an adjoint hypermultiplet. We study the refined open and
closed topological string partition functions of this geometry using the
refined topological vertex. We show that these partition functions, open and
closed, are examples of periodic Schur process and are related to the
generating function of the cylindric partitions if the Kahler parameters are
quantized in units of string coupling. The level-rank duality appears as the
exchange symmetry of the two Kahler parameters of the elliptic CY3-fold.
