{"product_id":"9780387985855","title":"Grundlehren der mathematischen Wissenschaften","description":"\u003ch1\u003eGrundlehren der mathematischen Wissenschaften\u003c\/h1\u003e \u003ch2\u003eConway, John; Sloane, Neil J. A.\u003c\/h2\u003e \u003cp\u003eWe 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1998-12-07\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387985855\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4757-6568-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 706\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44359145095308,"sku":"9780387985855","price":89.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387985855.jpg?v=1776434782","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780387985855","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}