Geodesic
Tiling Z² with translations of one set
Discrete mathematics & theoretical computer science, Tome 8 (2006).

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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. 
@article{DMTCS_2006_8_a7,
     author = {Rao, Hui and Xue, Yu-Mei},
     title = {Tiling {Z{\texttwosuperior}} with translations of one set},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {8},
     year = {2006},
     doi = {10.46298/dmtcs.366},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.366/}
}
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Rao, Hui; Xue, Yu-Mei. Tiling Z² with translations of one set. Discrete mathematics & theoretical computer science, Tome 8 (2006). doi : 10.46298/dmtcs.366. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.366/

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