The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.
The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.
Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related...
The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and...
This book is a groundbreaking work in the field of topology, exploring the properties of homotopy spheres and the various groups that can be derived from them. With detailed proofs and rigorous...
A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were...
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