A bijection for the total area of parallelogram polyominoes

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...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2004-12, Vol.144 (3), p.291-302
Main Authors: Del Lungo, Alberto, Nivat, Maurice, Pinzani, Renzo, Rinaldi, Simone
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Classical combinatorial problems
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Designs and configurations
Exact sciences and technology
Mathematics
Sciences and techniques of general use
Theoretical computing
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2003.11.007