On the Existence of Similar Sublattices
J. H. Conway
Mathematics Department
Princeton University
Princeton, NJ 08540
E. M. Rains and N. J. A. Sloane
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971
November 17, 1998; revised October 8, 1999.
A slightly different version of this paper appeared in the
Canadian Jnl. Math., {bf 51 (1999), pp. 1300-1306.
DEDICATED TO H. S. M. COXETER
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 boundary of the
Voronoi cells for Lambda ' do not intersect Lambda?
For the full version see
http://www.research.att.com/~njas/doc/sim.pdf (pdf) or
http://www.research.att.com/~njas/doc/sim.ps (ps)