Kevin Buchin, Man-Kwun Chiu, Stefan Felsner, Günter Rote, and André Schulz:

The number of convex polyominoes with given height and width

manuscript, April 2019, 18 pages, arXiv:1903.01095 [math.CO],  →BibTeX


We give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that contain the lower left corner of the enclosing rectangle (directed polyominoes). We indicate how to sample random polyominoes in these classes. As a side result, we calculate the first and second moments of the number of common points of two monotone lattice paths between two given points.

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Last update: March 5, 2019.