Variations on Tilings in the Manhattan Metric |
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Authors: | Gravier Sylvain Mollard Michel Payan Charles |
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Institution: | (1) CNRS, Laboratoire Leibniz, 46 avenue Félix Viallet, 38031 Grenoble Cedex 1, France |
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Abstract: | We investigate tilings of the integer lattice in the Euclidean n-dimensional space. The tiles considered here are the union of spheres defined by the Manhattan metric. We give a necessary condition for the existence of such a tiling for Z
n
when n 2. We prove that this condition is sufficient when n=2. Finally, we give some tilings of Z
n
when n 3. |
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Keywords: | tiling Manhattan metric |
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