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Tiling Z² with translations of one set

Abstract : 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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Hui Rao, Yu-Mei Xue. Tiling Z² with translations of one set. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2006, Vol. 8, pp.129--140. ⟨10.46298/dmtcs.366⟩. ⟨hal-00961116⟩



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