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On the Existence of Similar Sublattices

Published online by Cambridge University Press:  20 November 2018

J. H. Conway ,
E. M. Rains  and
N. J. A. Sloane
J. H. Conway
Affiliation:
Mathematics Department, Princeton University, Princeton, NJ 08540, USA
E. M. Rains
Affiliation:
Information Sciences Research, AT&T Shannon Lab, Florham Park, NJ 07932-0971, USA
N. J. A. Sloane
Affiliation:
Information Sciences Research, AT&T Shannon Lab, Florham Park, NJ 07932-0971, USA
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Abstract

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Partial answers are given to two questions. When does a lattice $\Lambda $ contain a sublattice ${\Lambda }'$ of index $N$ that is geometrically similar to $\Lambda $? When is the sublattice “clean”, in the sense that the boundaries of the Voronoi cells for ${\Lambda }'$ do not intersect $\Lambda $?

Keywords

52C07
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 6 , 01 December 1999 , pp. 1300 - 1306
Copyright
Copyright © Canadian Mathematical Society 1999

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