A Geometric Bijection for xy-Convex Curves and Convex Polyominoes |
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Authors: | Panov A. A. |
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Affiliation: | 1. Moscow State University of Geodesy and Cartography, Russia
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Abstract: | A connected subset of ${mathbb{R}}^2$ consisting of unit squares with integral vertices is called a convex polyomino or is simply said to be xy-convex if it intersects any horizontal or vertical line exactly in one closed interval. In this paper, a geometric representation for xy-convex sets is described, allowing us to obtain, by elementary combinatorial methods, known formulas for the number of convex polyominoes contained in a rectangle of given size. |
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