Finite packing and covering / Károly Böröczky, Jr.

Format:

Book

Author/Creator:

Böröczky, K., author.

Series:

Cambridge tracts in mathematics ; 154.

Cambridge tracts in mathematics ; 154

Language:

English

Subjects (All):

Combinatorial packing and covering.

Physical Description:

1 online resource (xvii, 380 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Finite Packing & Covering

Place of Publication:

Cambridge : Cambridge University Press, 2004.

Language Note:

English

Summary:

Finite arrangements of convex bodies were intensively investigated in the second half of the 20th century. Connections to many other subjects were made, including crystallography, the local theory of Banach spaces, and combinatorial optimisation. This book, the first one dedicated solely to the subject, provides an in-depth state-of-the-art discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments, besides collecting those scattered around in the literature, and provides a comprehensive treatment of problems whose interplay was not clearly understood before. In order to make the material more accessible, each chapter is essentially independent, and two-dimensional and higher-dimensional arrangements are discussed separately. Arrangements of congruent convex bodies in Euclidean space are discussed, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered.

Contents:

. Background

Part I. Arrangements in Two Dimensions:

g Congruent domains in the Euclidean plane

2. Translative arrangements

3. Parametric density

4. Packings of circular discs

5. Coverings by circular discs

Part II. Arrangements in Higher Dimensions

6. Packings and coverings by spherical balls

7. Congruent convex bodies

8. Packings and coverings by unit balls

9. Translative arrangements

10. Parametric density.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 357-377) and index.

ISBN:

1-107-14381-0

1-280-54104-0

9786610541041

0-511-21509-6

0-511-21688-2

0-511-21151-1

0-511-31556-2

0-511-54658-0

0-511-21328-X

OCLC:

171139070