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- Perfect_lattice abstract "In mathematics, a perfect lattice (or perfect form) is a lattice in a positive definite real vector space, that is determined by the set S of its minimal vectors in the sense that there is only one positive definite quadratic form taking value 1 at all points of S. A strongly perfect lattice is one whose minimal vectors form a spherical 4-design. Perfect lattices were introduced by Korkine & Zolotareff (1877).Voronoi (1908) proved that a lattice is extreme if and only if it is both perfect and eutactic. The number of perfect lattices in dimensions 1, 2, 3, 4, 5, 6, 7, 8 is given by 1, 1, 1, 2, 3, 7, 33, 10916 (sequence A004026 in OEIS). Conway & Sloane (1988) summarize the properties of perfect lattices of dimension up to 7.Sikirić, Schürmann & Vallentin (2007) verified that the list of 10916 perfect lattices in dimension 8 found by Martinet and others is complete. It was shown in Riener (2006) that only 2408 of these 10916 perfect lattices in dimension 8 are actually extreme lattices.".
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- Perfect_lattice wikiPageExternalLink lattice_geometry.
- Perfect_lattice wikiPageExternalLink 249637.
- Perfect_lattice wikiPageID "31985822".
- Perfect_lattice wikiPageRevisionID "584754884".
- Perfect_lattice hasPhotoCollection Perfect_lattice.
- Perfect_lattice subject Category:Quadratic_forms.
- Perfect_lattice type Abstraction100002137.
- Perfect_lattice type Form106290637.
- Perfect_lattice type LanguageUnit106284225.
- Perfect_lattice type Part113809207.
- Perfect_lattice type QuadraticForms.
- Perfect_lattice type Relation100031921.
- Perfect_lattice type Word106286395.
- Perfect_lattice comment "In mathematics, a perfect lattice (or perfect form) is a lattice in a positive definite real vector space, that is determined by the set S of its minimal vectors in the sense that there is only one positive definite quadratic form taking value 1 at all points of S. A strongly perfect lattice is one whose minimal vectors form a spherical 4-design.".
- Perfect_lattice label "Perfect lattice".
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- Perfect_lattice sameAs Perfect_lattice.
- Perfect_lattice wasDerivedFrom Perfect_lattice?oldid=584754884.
- Perfect_lattice isPrimaryTopicOf Perfect_lattice.