  Parallelogram polyominoes are a subclass of convex polyominoes in the square
lattice that has been studied extensively in the literature. Recently
congruence classes of convex polyominoes with respect to rotations and
reflections have been enumerated by counting orbits under the action of the
dihedral group D4, of symmetries of the square, on (translation-type) convex
polyominoes. Asymmetric convex polyominoes were also enumerated using Moebius
inversion in the lattice of subgroups of D4. Here we extend these results to
the subclass of parallelogram polyominos using a subgroup D2 of D4 which acts
of this class.
