Handbook of Combinatorial Designs

Handbook of Combinatorial Designs

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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.show more

Product details

  • Hardback | 1016 pages
  • 180.3 x 256.5 x 50.8mm | 1,791.71g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 300 black & white illustrations
  • 1584885068
  • 9781584885061
  • 1,067,206

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! Turan 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 INDEXshow more

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