Polyominoes which tile rectangles
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Packing rectangles with congruent polyominoes
Journal of Combinatorial Theory Series A
Tiling rectangles and half strips with congruent polyominoes
Journal of Combinatorial Theory Series A
Tiling a square with eight congruent polyominoes
Journal of Combinatorial Theory Series A
Discrete Mathematics
Selected combinatorial research problems.
Selected combinatorial research problems.
A finite basis theorem revisited.
A finite basis theorem revisited.
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Let I be a protoset of d-dimensional polyominoes. Which boxes (rectangular parallelepipeds) can be tiled by I? A nice result of Klarner and Göbel asserts that the answer to this question can always be given in a particularly simple form, namely, by giving a finite list of "prime" boxes. All other boxes that can be tiled can be deduced from these prime boxes. We give a new, simpler proof of this fundamental result. We also show that there is no upper bound to the number of prime boxes, even when restricting attention to singleton protosets. In the last section, we determine the set of prime rectangles for several small polyominoes.