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.
A bijection for the total area of parallelogram polyominoes / R. PINZANI; A. DEL LUNGO;M. NIVAT;S. RINALDI. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 144:(2004), pp. 291-302. [10.1016/j.dam.2003.11.007]
A bijection for the total area of parallelogram polyominoes
PINZANI, RENZO;
2004
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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