The sum of the areas of the parallelogram polyominoes having semi-perimeter n+2 is equal to 4^n. In this paper we give a simple proof of this property by means of a mapping from the cells of parallelogram polyominoes having semi-perimeter n+2 to the 4^n words of length n of the free monoid {a; b; c; d}^∗. This mapping works in linear time. Then, we introduce a tiling game arising from this enumerative property.
Del Lungo, A., Nivat, M., Pinzani, R., Rinaldi, S. (2004). A bijection for the total area of parallelogram polyominoes. DISCRETE APPLIED MATHEMATICS, 144(3), 291-302 [10.1016/j.dam.2003.11.007].
A bijection for the total area of parallelogram polyominoes
RINALDI, SIMONE
2004-01-01
Abstract
The sum of the areas of the parallelogram polyominoes having semi-perimeter n+2 is equal to 4^n. In this paper we give a simple proof of this property by means of a mapping from the cells of parallelogram polyominoes having semi-perimeter n+2 to the 4^n words of length n of the free monoid {a; b; c; d}^∗. This mapping works in linear time. Then, we introduce a tiling game arising from this enumerative property.
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https://hdl.handle.net/11365/10558
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