Sphere Packings, Lattices and Groups / by J. H. Conway, N. J. A. Sloane
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 290)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1993 |
| 本文言語 | 英語 |
| 大きさ | XLIII, 682 p. 3 illus : online resource |
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| 内容注記 | 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 |
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| 一般注記 | The second 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. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries |
| 著者標目 | *Conway, J. H. author Sloane, N. J. A. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Number theory LCSH:Combinatorics LCSH:Computational intelligence FREE:Mathematics FREE:Number Theory FREE:Combinatorics FREE:Computational Intelligence |
| 分 類 | DC23:512.7 |
| 巻冊次 | ISBN:9781475722499 
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| ISBN | 9781475722499 |
| URL | http://dx.doi.org/10.1007/978-1-4757-2249-9 |
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