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A Geometric Bijection for xy-Convex Curves and Convex Polyominoes

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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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Authors and Affiliations

  1. Moscow State University of Geodesy and Cartography, Russia

    A. A. Panov

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  1. A. A. Panov
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Panov, A.A. A Geometric Bijection for xy-Convex Curves and Convex Polyominoes. Mathematical Notes 74, 819–828 (2003). https://doi.org/10.1023/B:MATN.0000009018.28988.79

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  • DOI: https://doi.org/10.1023/B:MATN.0000009018.28988.79

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