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Enumeration of generalized polyominoes

Matthias Koch·Sascha Kurz
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Abstract

As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons. Additionally we give a table of the numbers $a_k(n)$ for small $k$ and $n$ obtained by computer enumeration. We finish with some open problems for $k$-polyominoes.

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Matthias Koch, Sascha Kurz. 2006-05-05. Enumeration of generalized polyominoes. https://arxiv.org/abs/math/0605144

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