Discrete Models for Complex Systems, DMCS'03
Michel Morvan and Éric Rémila (eds.)
DMTCS Conference Volume AB (2003), pp. 8188
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
. We show that, for each family of polycubes
d
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. 8188 
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