Sphere Packings, Lattices and Groups

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Sprache: Englisch

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Beschreibung

The third edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms.

Zusammenfassung

Inhaltsverzeichnis

1 Sphere Packings and Kissing Numbers.- 2 Coverings, Lattices and Quantizers.- 3 Codes, Designs and Groups.- 4 Certain Important Lattices and Their Properties.- 5 Sphere Packing and Error-Correcting Codes.- 6 Laminated Lattices.- 7 Further Connections Between Codes and Lattices.- 8 Algebraic Constructions for Lattices.- 9 Bounds for Codes and Sphere Packings.- 10 Three Lectures on Exceptional Groups.- 11 The Golay Codes and the Mathieu Groups.- 12 A Characterization of the Leech Lattice.- 13 Bounds on Kissing Numbers.- 14 Uniqueness of Certain Spherical Codes.- 15 On the Classification of Integral Quadratic Forms.- 16 Enumeration of Unimodular Lattices.- 17 The 24-Dimensional Odd Unimodular Lattices.- 18 Even Unimodular 24-Dimensional Lattices.- 19 Enumeration of Extremal Self-Dual Lattices.- 20 Finding the Closest Lattice Point.- 21 Voronoi Cells of Lattices and Quantization Errors.- 22 A Bound for the Covering Radius of the Leech Lattice.- 23 The Covering Radius of the Leech Lattice.- 24 Twenty-Three Constructions for the Leech Lattice.- 25 The Cellular Structure of the Leech Lattice.- 26 Lorentzian Forms for the Leech Lattice.- 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice.- 28 Leech Roots and Vinberg Groups.- 29 The Monster Group and its 196884-Dimensional Space.- 30 A Monster Lie Algebra?.- Supplementary Bibliography.

Details

Erscheinungsjahr:	2010
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	lxxiv 706 S.
ISBN-13:	9781441931344
ISBN-10:	1441931341
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Conway, John Sloane, Neil J. A.
Auflage:	Third Edition 1999
Hersteller:	Springer Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 42 mm
Von/Mit:	John Conway (u. a.)
Erscheinungsdatum:	01.12.2010
Gewicht:	1,165 kg