Sphere Packings, Lattices and Groups

Front Cover
Springer Science & Business Media, Mar 9, 2013 - Mathematics - 682 pages
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.
 

Contents

Chapter
1
1
8
3
24
Chapter 2
31
3
52
2
59
Chapter 4
94
6
114
12
316
18
327
Bounds on Kissing Numbers
337
Algebraic Constructions for Lattices
352
Rational Invariants of Quadratic Forms
370
9
387
7
393
11
400

2
124
The 24Dimensional Leech Lattice
131
6
139
4
145
Chapter 19
146
3
148
8
155
Chapter 13
157
The Main Results
162
Chapter 7
181
5
191
9
202
Chapter 23
220
3
227
2
233
Chapter 9
245
2
252
2
258
Chapter 10
267
5
279
3
287
Chapter 8
290
7
294
2
300
7
307
Chapter 16
406
Chapter 17
421
Chapter 20
443
Chapter 21
451
3
460
3
471
The Covering Radius of the Leech Lattice
476
Holes Whose Diagram Contains an A Subgraph
484
Chapter 18
494
Holes Whose Diagram Contains a D Subgraph
495
Holes Whose Diagram Contains an E Subgraph
502
The Cellular Structure of the Leech Lattice
513
The Enumeration of the Small Holes
519
Chapter 27
527
Enumeration of the Leech Roots
541
The Lattices I for n 19
547
The Monster Group and its 196884Dimensional Space
554
11
560
Chapter 30
568
Even Unimodular 24Dimensional Lattices
590
B B Venkov
632
427
657
3
666
5
672
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