Abstract
A cluster is the union of a finite number of cubes from the standard partition ofn-dimensional Euclidean space into unit cubes. If there is lattice tiling by translates of a cluster, then must there be a lattice tiling by translates of the cluster in which the translation vectors have only integer coordinates? In this article we prove that if the interior of the cluster is connected and the dimension is at most three, then the answer is affirmative.
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Szabó, S. A reduction of lattice tiling by translates of a cubical cluster. Discrete Comput Geom 2, 33–36 (1987). https://doi.org/10.1007/BF02187868
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DOI: https://doi.org/10.1007/BF02187868