Simple 2-Column Polyominoes on the Hexagonal Lattice
A simple 2-column polyomino is a polyomino in which every column has either one gap or no gaps and no two columns with a gap are next to each other. This Demonstration uses an extension of the generating function found by Svjetlan Feretic and Nenad Trinajstic both to count the number of polyominoes with each set of restrictions and to construct such a polyomino with uniform distribution. Setting the number of two-component columns to zero allows you to construct column-convex polygons.
The square lattice version was also solved in [1], however, both generating functions are too complicated to show here. For more information, see [2].
References
[1] S. Feretic and A. J. Guttmann, "Two Generalizations of Column-Convex Polygons," Journal of Physics A: Mathematical and Theoretical, 42(48), 2009. doi: 10.1088/1751-8113/42/485003.
[2] S. Feretic and N. Trinajstic, "The Area Generating Function for Simple-2-Column Polyomines with Hexagonal Cells," arXiv:0911.2527v1 [math.CO], 2009.
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