{"product_id":"sphere-packings-lattices-and-groups-book-john-conway-9780387985855","title":"Sphere Packings, Lattices and Groups","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49729535312145,"sku":"NGR9780387985855","price":0.0,"currency_code":"EUR","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50038224224529,"sku":"CIN0387985859VG","price":0.0,"currency_code":"EUR","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50628700307729,"sku":"GOR005301104","price":30.99,"currency_code":"EUR","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":51737827836177,"sku":"CIN0387985859G","price":0.0,"currency_code":"EUR","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52349152330001,"sku":"NLS9780387985855","price":0.0,"currency_code":"EUR","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52735282118929,"sku":"NIN9780387985855","price":0.0,"currency_code":"EUR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387985859.jpg?v=1751006766","url":"https:\/\/www.worldofbooks.com\/de-de\/products\/sphere-packings-lattices-and-groups-buch-john-conway-9780387985855","provider":"World of Books ","version":"1.0","type":"link"}