Handbook of Combinatorial Designs

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Charles J. Colbourn, Jeffrey H. Dinitz
CRC Press, Dec 12, 2010 - Mathematics - 1016 pages
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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.

     

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    Contents

    1 Opening the Door
    3
    Antiquity to 1950
    11
    1 2vk𝞴 Designs of Small Order
    25
    2 Triple Systems
    58
    3 BIBDs with Small Block Size
    72
    4 tDesigns with t 3
    79
    5 Steiner Systems
    102
    6 Symmetric Designs
    110
    26 Graphical Designs
    490
    27 Grooming
    494
    28 Hall Triple Systems
    496
    29 Howell Designs
    499
    30 Infinite Designs
    504
    Geometric Aspects
    506
    32 Lotto Designs
    512
    33 Low Density Parity Check Codes
    519

    7 Resolvable and NearResolvable Designs
    124
    1 Latin Squares
    135
    2 Quasigroups
    152
    3 Mutually Orthogonal Latin Squares MOLS
    160
    4 Incomplete MOLS
    193
    5 SelfOrthogonal Latin Squares SOLS
    211
    6 Orthogonal Arrays of Index More Than One
    219
    7 Orthogonal Arrays of Strength More Than Two
    224
    1 PBDs and GDDs The Basics
    231
    Recursive Constructions
    236
    3 PBDClosure
    247
    4 Group Divisible Designs
    255
    5 PBDs Frames and Resolvability
    261
    6 Pairwise Balanced Designs as Linear Spaces
    266
    1 Hadamard Matrices and Hadamard Designs
    273
    2 Orthogonal Designs
    280
    3 DOptimal Matrices
    296
    4 Bhaskar Rao Designs
    299
    5 Generalized Hadamard Matrices
    301
    6 Balanced Generalized Weighing Matrices and Conference Matrices
    306
    7 Sequence Correlation
    313
    8 Complementary Base and Turyn Sequences
    317
    9 Optical Orthogonal Codes
    321
    1 Association Schemes
    325
    2 Balanced Ternary Designs
    330
    3 Balanced Tournament Designs
    333
    4 Bent Functions
    337
    5 BlockTransitive Designs
    339
    6 Complete Mappings and Sequencings of Finite Groups
    345
    7 Configurations
    353
    8 CorrelationImmune and Resilient Functions
    355
    9 Costas Arrays
    357
    10 Covering Arrays
    361
    11 Coverings
    365
    12 Cycle Decompositions
    373
    13 Defining Sets
    382
    14 DeletionCorrecting Codes
    385
    15 Derandomization
    389
    16 Difference Families
    392
    17 Difference Matrices
    411
    18 Difference Sets
    419
    19 Difference Triangle Sets
    436
    20 Directed Designs
    441
    21 Factorial Designs
    445
    22 Frequency Squares and Hypercubes
    465
    23 Generalized Quadrangles
    472
    24 Graph Decompositions
    477
    25 Graph Embeddings and Designs
    486
    34 Magic Squares
    524
    35 Mendelsohn Designs
    528
    36 Nested Designs
    535
    Comparing Block Designs
    540
    38 Ordered Designs Perpendicular Arrays and Permutation Sets
    543
    39 Orthogonal Main Effect Plans
    547
    40 Packings
    550
    41 Partial Geometries
    557
    42 Partially Balanced Incomplete Block Designs
    562
    43 Perfect Hash Families
    566
    44 Permutation Codes and Arrays
    568
    45 Permutation Polynomials
    572
    46 Pooling Designs
    574
    47 Quasi3 Designs
    576
    48 QuasiSymmetric Designs
    578
    49 r λdesigns
    582
    50 Room Squares
    584
    51 Scheduling a Tournament
    591
    52 Secrecy and Authentication Codes
    606
    53 Skolem and Langford Sequences
    612
    54 Spherical Designs
    617
    55 Starters
    622
    56 Superimposed Codes and Combinatorial Group Testing
    629
    57 Supersimple Designs
    633
    58 Threshold and Ramp Schemes
    635
    59 tmsNets
    639
    60 Trades
    644
    61 Turán Systems
    649
    62 Tuscan Squares
    652
    63 tWise Balanced Designs
    657
    64 Whist Tournaments
    663
    65 Youden Squares and Generalized Youden Designs
    668
    1 Codes
    677
    2 Finite Geometry
    702
    3 Divisible Semiplanes
    729
    4 Graphs and Multigraphs
    731
    5 Factorizations of Graphs
    740
    6 Computational Methods in Design Theory
    755
    7 Linear Algebra and Designs
    783
    8 Number Theory and Finite Fields
    791
    9 Finite Groups and Designs
    819
    10 Designs and Matroids
    847
    11 Strongly Regular Graphs
    852
    12 Directed Strongly Regular Graphs
    868
    13 TwoGraphs
    875
    Bibliography
    883
    Index
    967
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