Discrete Mathematics & Theoretical Computer Science, Vol 8 (2006)

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Tile 2 with translations of one set

Hui Rao, Yu-mei Xue


Let A be a finite subset of ℤ2. We say A tiles ℤ2 with the translation set C, if any integer z∈ℤ2 can be represented as z1+z2, z1∈ A, z2∈ C in an unique way. In this case we call A a ℤ2-tile and write A ⊕ C = ℤ2. A tile A is said to be a normal ℤ2-tile if there exists a periodic set C such that A ⊕ C = ℤ2. We characterize all normal ℤ2-tiles with prime cardinality.

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