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Sphere Packings, Lattices and Groups
Conway, J. H ; Sloane, N. J. A ; Bannai, E ; Borcherds, R. E ; Leech, J ; Norton, S. P ; Odlyzko, A. M ; Parker, R. A ; Queen, L ; Venkov, B. B
New York, NY: Springer 1992
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Título:
Sphere Packings, Lattices and Groups
Autor:
Conway, J. H
;
Sloane, N. J. A
;
Bannai, E
;
Borcherds, R. E
;
Leech, J
;
Norton, S. P
;
Odlyzko, A. M
;
Parker, R. A
;
Queen, L
;
Venkov, B. B
Assuntos:
Chemistry
;
Combinatorics
;
Computational Intelligence
;
Engineering
;
Group theory
;
Group Theory and Generalizations
;
Math. Applications in Chemistry
;
Mathematics
;
Number theory
;
Sphere packings
;
Theoretical, Mathematical and Computational Physics
Descrição:
The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.
Títulos relacionados:
Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
Editor:
New York, NY: Springer
Data de criação/publicação:
1992
Formato:
724
Idioma:
Inglês
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