DMTCS Proceedings, Discrete Models for Complex Systems, DMCS'03

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DMTCS Conference vol AB (2003), pp. 81-88

DMTCS

Discrete Models for Complex Systems, DMCS'03

Michel Morvan and Éric Rémila (eds.)

DMTCS Conference Volume AB (2003), pp. 81-88


author: Olivier Bodini
title: Tiling a Rectangle with Polyominoes
keywords: Tiling, Polyomino
abstract: A polycube in dimension d is a finite union of unit
d
-cubes whose vertices are on knots of the lattice
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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reference: Olivier Bodini (2003), Tiling a Rectangle with Polyominoes, in Discrete Models for Complex Systems, DMCS'03, Michel Morvan and Éric Rémila (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AB, pp. 81-88
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