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null Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Penttila, Tim / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Sommese, Andrew J. / Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard / Rosehr, Nils / Bannai, Eiichi
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1Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/1046, 1040 Vienna, Austria
Citation Information: Advances in Geometry. Volume 11, Issue 4, Pages 691–710, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom.2011.024, August 2011
Publication History:
For d = 2, 3 a generic convex body in 
has a unique lattice packing and for d ≥ 4 at most a(d) lattice packings of maximum density, where a(d) ≥ 1 is a constant. If in a certain connectedness property holds, one may take a(d) = 1. Dually, for d = 2 a generic convex body has a unique lattice covering of minimum density and for d ≥ 3 there is a constant b(d) ≥ 1 such that it has at most b(d) such coverings.
Key words.: Convex body; lattice packing; lattice covering; extreme density; extreme lattice; uniqueness; Baire categories
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