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  On the existence of similar sublattices (1999) [20 citations — 7 self]

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by J. H. Conway, E. M. Rains, N. J. A. Sloane
Canad. J. Math
http://www.research.att.com/~njas/doc/sim.ps
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Abstract:

Partial answers are given to two questions. When does a lattice contain a sublattice 0 of index N that is geometrically similar to? When is the sublattice "clean", in the sense that the boundary of the Voronoi cells for 0

Citations

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21 Multiple description lattice vector quantization – Servetto, Vaishampayan, et al. - 1999
21 Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis – Vaishampayan, Sloane, et al. - 2001
11 Planar coincidences for N-fold symmetry – Pleasants, Baake, et al. - 1996
8 Algebraic solution of the coincidence problem in two and three dimensions, Z. Naturforschung 50A – Baake, Pleasants - 1995
8 Low-dimensional lattices I: Quadratic forms of small determinant – Conway, Sloane - 1988
7 Similarity Submodules and Semigroups – Baake, Moody - 1998
7 Arithmetic of Quadratic Forms – Kitaoka - 1993
6 Similarity submodules and root systems in four dimensions – Baake, Moody - 1999
6 Integral quadratic forms – Watson - 1960
5 Solution of the coincidence problem in dimensions d ≤ 4 – Baake - 1997
4 Low-dimensional lattices VI: Voronoi reduction of three-dimensional lattices – Conway, Sloane - 1992
3 The coincidence problem for crystals and quasicrystals – Baake, Pleasants - 1995
2 On the expression of a number in the form ax2 – Ramanujan - 1927
1 Shrinking integer lattices – Chapman - 1995
1 On the expression of a number in the form ax + by + cz + du – Ramanujan - 1927
1 On the expression of a number in the form ax 2 + by 2 + cz 2 – Ramanujan - 1927
1 Shrinking integer lattices, Discrete Math. 142 – Chapman - 1995
1 Arithmetic of Quadratic Forms, Cambridge Univ – Kitaoka - 1993