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Thin non-lattice covering with an affine image of a strictly convex body

Part of: Discrete geometry

Published online by Cambridge University Press:  26 February 2010

Gábor Fejes Tóth  and
Wlodzimierz Kuperberg
Gábor Fejes Tóth
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary.
Wlodzimierz Kuperberg
Affiliation:
Department of Mathematics, Auburn University, AL 36849-5310, U.S.A.
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Abstract

We prove that for every strictly convex body C in the Euclidean space of dimension d≥3, some aflfine image of C admits a non-lattice covering of the space, thinner than any lattice covering. We illustrate the general construction with an example of a thin non-lattice covering of with certain congruent ellipsoids.

MSC classification

Secondary: 52C17: Packing and covering in $n$ dimensions
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 239 - 250
Copyright
Copyright © University College London 1995

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