Rao, Hui and Xue, Yu-Mei - Tiling Z² with translations of one set

dmtcs:366 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, Vol. 8
Tiling Z² with translations of one set

Authors: Rao, Hui and Xue, Yu-Mei

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.


Volume: Vol. 8
Published on: January 1, 2006
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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