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Constructive packings of cross polytopes

Part of: Geometry of numbers

Published online by Cambridge University Press:  26 February 2010

J. A. Rush
J. A. Rush
Affiliation:
Professor J. A. Rush, Department of Mathematics, GN-50, University of Washington, Seattle, Washington 98195, U.S.A.
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Abstract

The n-dimensional cross polytope, |x|+|x2|+…+|xn≤1, can be lattice packed with density δ satisfying

but proofs of this, such as the Minkowski-Hlawka theorem, do not actually provide such packings. That is, they are nonconstructive. Here we exhibit lattice packings whose density satisfies only

but by a highly constructive method. These are the densest constructive lattice packings of cross polytopes obtained so far.

MSC classification

Secondary: 11H31: Lattice packing and covering
Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 376 - 380
Copyright
Copyright © University College London 1991

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