Enumeration of generalized polyominoes

Details Enumeration of generalized polyominoes Enumeration of generalized polyominoes

2006-05-05

arxiv.org/abs/math/0605144v1

Mathematics

Combinatorics

10 pages, 6 figures, 3 tables

Scientific paper

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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