Grundlehren der mathematischen Wissenschaften

Sphere Packings, Lattices and Groups

Authors: Conway, John, Sloane, Neil J. A.

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We now apply the algorithm above to find the 121 orbits of norm -2 vectors from the (known) nann 0 vectors, and then apply it again to find the 665 orbits of nann -4 vectors from the vectors of nann 0 and -2. The neighbors of a strictly 24 dimensional odd unimodular lattice can be found as follows. If a norm -4 vector v E II . corresponds to the sum 25 1 of a strictly 24 dimensional odd unimodular lattice A and a !-dimensional lattice, then there are exactly two nonn-0 vectors of ll25,1 having inner product -2 with v, and these nann 0 vectors correspond to the two even neighbors of A. The enumeration of the odd 24-dimensional lattices. Figure 17.1 shows the neighborhood graph for the Niemeier lattices, which has a node for each Niemeier lattice. If A and B are neighboring Niemeier lattices, there are three integral lattices containing A n B, namely A, B, and an odd unimodular lattice C (cf. [Kne4]). An edge is drawn between nodes A and B in Fig. 17.1 for each strictly 24-dimensional unimodular lattice arising in this way. Thus there is a one-to-one correspondence between the strictly 24-dimensional odd unimodular lattices and the edges of our neighborhood graph. The 156 lattices are shown in Table 17 .I. Figure I 7. I also shows the corresponding graphs for dimensions 8 and 16.

Reviews

Third Edition

J.H. Conway and N.J.A. Sloane

Sphere Packings, Lattices and Groups

"This is the third edition of this reference work in the literature on sphere packings and related subjects. In addition to the content of the preceding editions, the present edition provides in its preface a detailed survey on recent developments in the field, and an exhaustive supplementary bibliography for 1988-1998. A few chapters in the main text have also been revised."—MATHEMATICAL REVIEWS

• Sphere Packings and Kissing Numbers

Conway, J. H. (et al.)

Pages 1-30

30,19 €
• Coverings, Lattices and Quantizers

Conway, J. H. (et al.)

Pages 31-62

30,19 €
• Codes, Designs and Groups

Conway, J. H. (et al.)

Pages 63-93

30,19 €
• Certain Important Lattices and Their Properties

Conway, J. H. (et al.)

Pages 94-135

30,19 €
• Sphere Packing and Error-Correcting Codes

Leech, John (et al.)

Pages 136-156

30,19 €

eBook 66,99 €
price for Spain (gross)
valid through March 31, 2018
• ISBN 978-1-4757-6568-7
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices
Hardcover 84,19 €
price for Spain (gross)
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• ISBN 978-0-387-98585-5
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.
• The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 84,19 €
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• ISBN 978-1-4419-3134-4
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Sphere Packings, Lattices and Groups
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
290
1999
Publisher
Springer-Verlag New York
eBook ISBN
978-1-4757-6568-7
DOI
10.1007/978-1-4757-6568-7
Hardcover ISBN
978-0-387-98585-5
Softcover ISBN
978-1-4419-3134-4
Series ISSN
0072-7830
Edition Number
3
Number of Pages
LXXIV, 706
Topics