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Tiling a Rectangle with Polyominoes
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Tiling a Rectangle with Polyominoes

Olivier Bodini
Discrete Mathematics and Theoretical Computer Science, Vol.DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), pp.81-88
DMTCS Proceedings
Discrete Models for Complex Systems, DMCS'03 (Lyon, France, 2003)
01/01/2003

Résumé

Polyomino Tiling
A polycube in dimension $d$ is a finite union of unit $d$-cubes whose vertices are on knots of the lattice $\mathbb{Z}^d$. We show that, for each family of polycubes $E$, there exists a finite set $F$ of bricks (parallelepiped rectangles) such that the bricks which can be tiled by $E$ are exactly the bricks which can be tiled by $F$. Consequently, if we know the set $F$, then we have an algorithm to decide in polynomial time if a brick is tilable or not by the tiles of $E$.

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