Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice *

  title={Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice *},
  author={Pierre Leroux and Etienne Rassart and Arnaud Robitaille},
This paper concerns the enumeration of rotation-type and congruence-type convex polyominoes on the square lattice. These can be defined as orbits of the groups C4, of rotations, and D4, of symmetries, of the square, acting on (translation-type) polyominoes. In virtue of Burnside’s Lemma, it is sufficient to enumerate the various symmetry classes (fixed points) of polyominoes defined by the elements of C4 and D4. Using the Temperley–Bousquet-Mélou methodology, we solve this problem and provide… CONTINUE READING
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