Geodesic
Tiling a Rectangle with Polyominoes
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03) (2003).

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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 $E$. 
@article{DMTCS_2003_special_247_a12,
     author = {Bodini, Olivier},
     title = {Tiling a {Rectangle} with {Polyominoes}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03)},
     year = {2003},
     doi = {10.46298/dmtcs.2313},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2313/}
}
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Bodini, Olivier. Tiling a Rectangle with Polyominoes. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03) (2003). doi : 10.46298/dmtcs.2313. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2313/

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