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A lattice without a basis of minimal vectors

Part of: Geometry of numbers

Published online by Cambridge University Press:  26 February 2010

J. H. Conway  and
N. J. A. Sloane
J. H. Conway
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544, U.S.A.
N. J. A. Sloane
Affiliation:
Mathematical Sciences Research Center, AT&T Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.
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Abstract

It is shown that in all dimensions n ≥ 11 there exists a lattice which is generated by its minimal vectors but in which no set of n minimal vectors forms a basis.

MSC classification

Secondary: 11H99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 175 - 177
Copyright
Copyright © University College London 1995

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References

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