A criterion for finite lattice coverings |
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Authors: | Schnell Uwe Schürmann Achill |
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Institution: | (1) Mathematical Institute, University of Siegen, D-57068 Siegen, Germany |
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Abstract: | For a centrally symmetric convex
and a covering lattice L for K, a lattice polygon P is called a covering polygon, if
. We prove that P is a covering polygon, if and only if its boundary bd(P) is covered by (L ∩ P) + K. Further we show that this characterization is false for non-symmetric planar convex bodies and
in Euclidean d–space, d ≥ 3, even for the unit ball K = B
d.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | lattice covering convex body |
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