  We construct a free fermion and matrix model representation of refined BPS
generating functions of D2 and D0 branes bound to a single D6 brane, in a class
of toric manifolds without compact four-cycles. In appropriate limit we obtain
a matrix model representation of refined topological string amplitudes. We
consider a few explicit examples which include a matrix model for the refined
resolved conifold, or equivalently five-dimensional U(1) gauge theory, as well
as a matrix representation of the refined MacMahon function. Matrix models
which we construct have ordinary unitary measure, while their potentials are
modified to incorporate the effect of the refinement.
