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On the Existence of Similar Sublattices |
Canad. J. Math. 51(1999), 1300-1306
Published:1999-12-01
Printed: Dec 1999
Printed: Dec 1999
- J. H. Conway
- E. M. Rains
- N. J. A. Sloane
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] |