{"product_id":"sphere-packings-lattices-and-groups-grundlehren-der-mathematischen-wissenschaften-290-0387985859","title":"Sphere Packings, Lattices and Groups (Grundlehren der mathematischen Wissenschaften, 290)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0387985859\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Conway, John\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\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","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51855765078304,"sku":"NEW0387985859","price":100.8,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/51lpSxJADLL.jpg?v=1781541045","url":"https:\/\/miakarts.com\/products\/sphere-packings-lattices-and-groups-grundlehren-der-mathematischen-wissenschaften-290-0387985859","provider":"Miakarts Books","version":"1.0","type":"link"}