Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice
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Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyominoes, according to area and half-perimeter. We give explicit formulas or implicit functional equations for the generating series, which are convenient for computer algebra.
21 pages, 16 figures, 2 tables. This is the full version of a paper presented at the FPSAC Conference in Vancouver, Canada, June 28 -- July 2, 2004
21 pages, 16 figures, 2 tables. This is the full version of a paper presented at the FPSAC Conference in Vancouver, Canada, June 28 -- July 2, 2004