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Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften, 290) by J. H. Conway, N. J. A. Sloane (auth.) is a nonfiction available to read on EtoBox.

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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 ar

Who reads Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften, 290)?

Author

J. H. Conway, N. J. A. Sloane (auth.)

Publisher

Springer-Verlag New York

Published

1999

Language

EN

ISBN

9781475765687

Category

nonfiction

Subjects

Mathematics, Engineering, Computer Science

Updated

2026-03-24