On the existence of similar sublattices

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Abstract

Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λ′ of index N that is geometrically similar to Λ? When is the sublattice "clean", in the sense that the boundaries of the Voronoi cells for Λ′ do not intersect Λ?

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Conway, J. H., Rains, E. M., & Sloane, N. J. A. (1999). On the existence of similar sublattices. Canadian Journal of Mathematics, 51(6), 1300–1306. https://doi.org/10.4153/CJM-1999-059-5

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