  We study the partition function of the compactified 5D U(1) gauge theory (in
the Omega-background) with a single adjoint hypermultiplet, calculated using
the refined topological vertex. We show that this partition function is an
example a periodic Schur process and is a refinement of the generating function
of cylindric plane partitions. The size of the cylinder is given by the mass of
adjoint hypermultiplet and the parameters of the Omega-background. We also show
that this partition function can be written as a trace of operators which are
generalizations of vertex operators studied by Carlsson and Okounkov. In the
last part of the paper we describe a way to obtain (q,t) identities using the
refined topological vertex.
