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

dmtcs:366 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, Vol. 8 - https://doi.org/10.46298/dmtcs.366
Tiling Z² with translations of one set

Authors: 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.


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

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