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      Death and Mr. Pickwick

      Stephen Jarvis 9780374139667

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25 Remote Warehouse Mathematics- Logic and Philosophy

Other titles in the Grundlehren Der Mathematischen Wissenschaften series:

Perfect Lattices in Euclidean Spaces

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Perfect Lattices in Euclidean Spaces Cover

 

Synopses & Reviews

Publisher Comments:

Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.

Synopsis:

Includes bibliographical references (p. [497]-509) and index.

Table of Contents

General Properties of Lattices.- Geometric Inequalities.- Perfection and Eutaxy.- Root Lattices.- Lattices Related to Root Lattices.- Low-Dimensional Perfect Lattices.- The Voronoi Algorithm.- Hermitian Lattices.- The Configurations of Minimal Vectors.- Extremal Properties of Families of Lattices.- Group Actions.- Cross-Sections.- Extensions of the Voronoi Algorithm.- Numerical Data.- Appendix 1: Semi-Simple Algebras and Quaternions.- Appendix 2: Strongly Perfect Lattices.

Product Details

ISBN:
9783540442363
Author:
Martinet, Jacques
Publisher:
Springer
Author:
Zhang, Wei-Bin D.
Author:
Zhang, Wei-Bin D.
Location:
Berlin, Heidelberg
Subject:
General
Subject:
Logic
Subject:
Discrete Mathematics
Subject:
Lattice theory
Subject:
Vector spaces
Subject:
Combinatorial packing and covering
Subject:
Number Theory
Subject:
Euclidean lattices
Subject:
eutactic lattices
Subject:
perfect lattices
Subject:
Sphere packings
Subject:
Combinatorics
Subject:
Combinatorics <P>&nbsp;Long-awaited authoritative reference on this beautiful subject at the interface&nbsp;of geometry, number theory, coding theory and group theory</P> <P>Complement to J.H. Conway and N.J.A. Sloane "Sphere Packings, Lattices and Groups
Subject:
Mathematics-Logic and Philosophy
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
Book
Series:
Grundlehren der mathematischen Wissenschaften,
Series Volume:
1.327
Publication Date:
20030212
Binding:
HARDCOVER
Language:
English
Pages:
541
Dimensions:
235 x 155 mm 2100 gr

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Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Logic and Philosophy

Perfect Lattices in Euclidean Spaces New Hardcover
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Product details 541 pages Springer - English 9783540442363 Reviews:
"Synopsis" by , Includes bibliographical references (p. [497]-509) and index.
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