Enumeration of Symmetry Classes of Parallelogram Polyominoes

Details Enumeration of Symmetry Classes of Parallelogram Polyominoes Enumeration of Symmetry Classes of Parallelogram Polyominoes

1999-01-28

arxiv.org/abs/math/9901135v1

Annales des Sciences mathematiques du Quebec, 25 (2001), 71-90

Mathematics

Combinatorics

LaTeX 2e, 14 pages with 10 figures

Scientific paper

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.

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