Enumeration of generalized polyominoes

الأصل · EN

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