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# On the Existence of Similar Sublattices

Published:1999-12-01
Printed: Dec 1999
• J. H. Conway
• E. M. Rains
• N. J. A. Sloane
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## Abstract

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 $\Lambda$?
 MSC Classifications: 52C07 - Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]