Klein polyhedra and relative minima of lattices |
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Authors: | O N German |
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Institution: | (1) M. V. Lomonosov Moscow State University, Russia |
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Abstract: | We prove that in ?3, the relative minima of almost any lattice belong to the surface of the corresponding Klein polyhedron. We also prove, for almost any lattice in ?3, that the set of relative minima with nonnegative coordinates coincides with the union of the set of extremal points of the Klein polyhedron and a set of special points belonging to the triangular faces of the Klein polyhedron. |
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Keywords: | lattice multidimensional continued fraction Klein polyhedron |
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