Parallelogram polyominoes are a subclass of convex polyominoes in the squarelattice that has been studied extensively in the literature. Recentlycongruence classes of convex polyominoes with respect to rotations andreflections have been enumerated by counting orbits under the action of thedihedral group D4, of symmetries of the square, on (translation-type) convexpolyominoes. Asymmetric convex polyominoes were also enumerated using Moebiusinversion in the lattice of subgroups of D4. Here we extend these results tothe subclass of parallelogram polyominos using a subgroup D2 of D4 which actsof this class.
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