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1 LIRMM - Laboratoire d-Informatique de Robotique et de Microélectronique de Montpellier

Abstract : 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 $E$.

Keywords : Tiling Polyomino

Author: Olivier Bodini -

Source: https://hal.archives-ouvertes.fr/


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