2nd Edition

Handbook of Combinatorial Designs

Edited By Charles J. Colbourn, Jeffrey H. Dinitz Copyright 2007
    1016 Pages 300 B/W Illustrations
    by Chapman & Hall

    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.


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

    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
    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

    PBDs and GDDs: The Basics
    PBDs: Recursive Constructions
    NEW! Group Divisible Designs
    PBDs, Frames, and Resolvability
    Pairwise Balanced Designs as Linear Spaces

    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

    Association Schemes
    Balanced Ternary Designs
    Balanced Tournament Designs
    NEW! Bent Functions
    NEW! Block-Transitive Designs
    Complete Mappings and Sequencings of Finite Groups
    Correlation-Immune and Resilient Functions
    Costas Arrays
    NEW! Covering Arrays
    Cycle Decompositions
    Defining Sets
    NEW! Deletion-Correcting Codes
    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
    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
    Superimposed Codes and Combinatorial Group Testing
    NEW! Supersimple Designs
    Threshold and Ramp Schemes
    NEW! Turán Systems
    Tuscan Squares
    t-Wise Balanced Designs
    Whist Tournaments
    Youden Squares and Generalized Youden Designs

    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



    Charles J. Colbourn, Jeffrey H. Dinitz

    ". . . 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