A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Regular Article: Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice
Advances in Applied Mathematics
Area limit laws for symmetry classes of staircase polygons
Combinatorics, Probability and Computing
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We enumerate the symmetry classes of convex polyominoes on the hexagonal (honeycomb) lattice. 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. Thus, computations can be carried out up to area 70.