Handbook of Combinatorial Designs: 2nd Edition (Hardback) book cover

Handbook of Combinatorial Designs

2nd Edition

Edited by Charles J. Colbourn, Jeffrey H. Dinitz

Chapman and Hall/CRC

1,016 pages | 300 B/W Illus.

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pub: 2006-11-02
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Description

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.

    Reviews

    ". . . remains the only resource to contain all of the most important results and tables in the field of combinatorial design."

    – In L’Enseignement Mathématique, January-June 2007, Vol. 53, No. 1-2

    Table of Contents

    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

    About the Series

    Discrete Mathematics and Its Applications

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    COM046000
    COMPUTERS / Operating Systems / General
    COM051300
    COMPUTERS / Programming / Algorithms
    MAT036000
    MATHEMATICS / Combinatorics