Sphere Packings, Lattices and Groups Hardback
by John Conway, Neil J. A. Sloane
Part of the Grundlehren der mathematischen Wissenschaften series
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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.
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In Stock - Less than 10 copies availableFree UK DeliveryEstimated delivery 2-3 working days
- Format:Hardback
- Pages:706 pages, LXXIV, 706 p.
- Publisher:Springer-Verlag New York Inc.
- Publication Date:07/12/1998
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- ISBN:9780387985855
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In Stock - Less than 10 copies availableFree UK DeliveryEstimated delivery 2-3 working days
- Format:Hardback
- Pages:706 pages, LXXIV, 706 p.
- Publisher:Springer-Verlag New York Inc.
- Publication Date:07/12/1998
- Category:
- ISBN:9780387985855