A bijection for the total area of parallelogram polyominoes Original Research Article

The sum of the areas of the parallelogram polyominoes having semi-perimeter n+2 is equal to 4n. 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 4n 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.