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Abstract: Column-convex polyominoes are by now a well-explored model. So far, however,no attention has been given to polyominoes whose columns can have either one ortwo connected components. This little known kind of polyominoes seems not to bemanageable as a whole. To obtain solvable models, one needs to introduce somerestrictions. This paper is focused on polyominoes with hexagonal cells. Therestrictions just mentioned are semidirectedness and an upper bound on the sizeof the gap within a column. The solvable models so obtained have rational areagenerating functions, as column-convex polyominoes do. However, the growthconstants of the new models are 4.114908 and more, whereas the growth constantof column-convex polyominoes is 3.863131.



Author: Svjetlan Feretic

Source: https://arxiv.org/



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