Colbourn / Dinitz Handbook of Combinatorial Designs, Second Edition

2. Auflage 2010
ISBN: 978-1-4398-3234-9
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 1016 Seiten

Reihe: Discrete Mathematics and Its Applications

Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results.

Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory.

New to the Second Edition
- An introductory part that provides a general overview and a historical perspective of the area

- New chapters on the history of design theory, various codes, bent functions, and numerous types of designs

- Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices

- Nearly 2,200 references in a single bibliographic section

Meeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline.

The author maintains a website with more information.

Zielgruppe

Researchers and students in combinatorial design theory; mathematicians, statisticians, computer scientists, and engineers who use combinatorial mathematics in computing, networking, communications, and cryptography.

Autoren/Hrsg.

Colbourn, Charles J.

Dinitz, Jeffrey H.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Kryptologie, Informationssicherheit
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung

Inhaltsverzeichnis

PREFACE

INTRODUCTION
NEW! Opening the Door
NEW! Design Theory: Antiquity to 1950

BLOCK DESIGNS
2-(v, k, ?) Designs of Small Order
NEW! Triple Systems
BIBDs with Small Block Size
t-Designs with t = 3
Steiner Systems
Symmetric Designs
Resolvable and Near-Resolvable Designs

LATIN SQUARES
Latin Squares
Quasigroups
Mutually Orthogonal Latin Squares (MOLS)
Incomplete MOLS
Self-Orthogonal Latin Squares (SOLS)
Orthogonal Arrays of Index More Than One
Orthogonal Arrays of Strength More Than Two

PAIRWISE BALANCED DESIGNS
PBDs and GDDs: The Basics
PBDs: Recursive Constructions
PBD-Closure
NEW! Group Divisible Designs
PBDs, Frames, and Resolvability
Pairwise Balanced Designs as Linear Spaces

HADAMARD MATRICES AND RELATED DESIGNS
Hadamard Matrices and Hadamard Designs
Orthogonal Designs
D-Optimal Matrices
Bhaskar Rao Designs
Generalized Hadamard Matrices
Balanced Generalized Weighing Matrices and Conference Matrices
Sequence Correlation
Complementary, Base and Turyn Sequences
NEW! Optical Orthogonal Codes

OTHER COMBINATORIAL DESIGNS
Association Schemes
Balanced Ternary Designs
Balanced Tournament Designs
NEW! Bent Functions
NEW! Block-Transitive Designs
Complete Mappings and Sequencings of Finite Groups
Configurations
Correlation-Immune and Resilient Functions
Costas Arrays
NEW! Covering Arrays
Coverings
Cycle Decompositions
Defining Sets
NEW! Deletion-Correcting Codes
Derandomization
Difference Families
Difference Matrices
Difference Sets
Difference Triangle Sets
Directed Designs
Factorial Designs
Frequency Squares and Hypercubes
Generalized Quadrangles
Graph Decompositions
NEW! Graph Embeddings and Designs
Graphical Designs
NEW! Grooming
Hall Triple Systems
Howell Designs
NEW! Infinite Designs
Linear Spaces: Geometric Aspects
Lotto Designs
NEW! Low Density Parity Check Codes
NEW! Magic Squares
Mendelsohn Designs
NEW! Nested Designs
Optimality and Efficiency: Comparing Block Designs
Ordered Designs, Perpendicular Arrays and Permutation Sets
Orthogonal Main Effect Plans
Packings
Partial Geometries
Partially Balanced Incomplete Block Designs
NEW! Perfect Hash Families
NEW! Permutation Codes and Arrays
NEW! Permutation Polynomials
NEW! Pooling Designs
NEW! Quasi-3 Designs
Quasi-Symmetric Designs
(r, ?)-designs
Room Squares
Scheduling a Tournament
Secrecy and Authentication Codes
Skolem and Langford Sequences
Spherical Designs
Starters
Superimposed Codes and Combinatorial Group Testing
NEW! Supersimple Designs
Threshold and Ramp Schemes
(t,m,s)-Nets
Trades
NEW! Turán Systems
Tuscan Squares
t-Wise Balanced Designs
Whist Tournaments
Youden Squares and Generalized Youden Designs

RELATED MATHEMATICS
Codes
Finite Geometry
NEW! Divisible Semiplanes
Graphs and Multigraphs
Factorizations of Graphs
Computational Methods in Design Theory
NEW! Linear Algebra and Designs
Number Theory and Finite Fields
Finite Groups and Designs
NEW! Designs and Matroids
Strongly Regular Graphs
NEW! Directed Strongly Regular Graphs
Two-Graphs

BIBLIOGRAPHY
INDEX