On the Existence of Similar Sublattices

Mathematics – Combinatorics

Scientific paper

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7 pages; dedicated to H.S.M. Coxeter

Scientific paper

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?

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