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Handbook of Combinatorial Designs

Edited by: Charles J. Colbourn , Jeffrey H. Dinitz

Print publication date:  November  2006
Online publication date:  November  2006

Print ISBN: 9781584885061
eBook ISBN: 9781420010541
Adobe ISBN:

10.1201/9781420010541
 Cite  Marc Record

Book description

Continuing in the bestselling, informative tradition of the first edition, the <strong>Handbook of Combinatorial Designs, Second Edition</strong> 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.<BR><BR>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.<BR><BR>New to the Second Edition<BR><li>An introductory part that provides a general overview and a historical perspective of the area<BR></li><li>New chapters on the history of design theory, various codes, bent functions, and numerous types of designs<BR></li><li>Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices<BR></li><li>Nearly 2,200 references in a single bibliographic section<BR><BR>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.</li><p> The author maintains a <a href="http://www.cems.uvm.edu/~dinitz/hcd.html" target="_blank">website with more information</a>.

Table of contents

Prelims Download PDF
Chapter  1:  Opening the Door Download PDF
Chapter  2:  Design Theory: Antiquity to 1950 Download PDF
Chapter  3:  2-(v, k, λ) Designs of Small Order Download PDF
Chapter  4:  Triple Systems Download PDF
Chapter  5:  BIBDs with Small Block Size Download PDF
Chapter  6:  t-Designs with t ≥ 3 Download PDF
Chapter  7:  Steiner Systems Download PDF
Chapter  8:  Symmetric Designs Download PDF
Chapter  9:  Resolvable and Near-Resolvable Designs Download PDF
Chapter  10:  Latin Squares Download PDF
Chapter  11:  Quasigroups Download PDF
Chapter  12:  Mutually Orthogonal Latin Squares (MOLS) Download PDF
Chapter  13:  Incomplete MOLS Download PDF
Chapter  14:  Self-Orthogonal Latin Squares (SOLS) Download PDF
Chapter  15:  Orthogonal Arrays of Index More Than One Download PDF
Chapter  16:  Orthogonal Arrays of Strength More Than Two Download PDF
Chapter  17:  PBDs and GDDs: The Basics Download PDF
Chapter  18:  PBDs: Recursive Constructions Download PDF
Chapter  19:  PBD-Closure Download PDF
Chapter  20:  Group Divisible Designs Download PDF
Chapter  21:  PBDs, Frames, and Resolvability Download PDF
Chapter  22:  Pairwise Balanced Designs as Linear Spaces Download PDF
Chapter  23:  Hadamard Matrices and Hadamard Designs Download PDF
Chapter  24:  Orthogonal Designs Download PDF
Chapter  25:  D-Optimal Matrices Download PDF
Chapter  26:  Bhaskar Rao Designs Download PDF
Chapter  27:  Generalized Hadamard Matrices Download PDF
Chapter  28:  Balanced Generalized Weighing Matrices and Conference Matrices Download PDF
Chapter  29:  Sequence Correlation Download PDF
Chapter  30:  Complementary, Base, and Turyn Sequences Download PDF
Chapter  31:  Optical Orthogonal Codes Download PDF
Chapter  32:  Association Schemes Download PDF
Chapter  33:  Balanced Ternary Designs Download PDF
Chapter  34:  Balanced Tournament Designs Download PDF
Chapter  35:  Bent Functions Download PDF
Chapter  36:  Block-Transitive Designs Download PDF
Chapter  37:  Complete Mappings and Suencings of Finite Groups Download PDF
Chapter  38:  Configurations Download PDF
Chapter  39:  Correlation-immune and Resilient Functions Download PDF
Chapter  40:  Costas Arrays Download PDF
Chapter  41:  Covering Arrays Download PDF
Chapter  42:  Coverings Download PDF
Chapter  43:  Cycle Decompositions Download PDF
Chapter  44:  Defining Sets Download PDF
Chapter  45:  Deletion-correcting Codes Download PDF
Chapter  46:  Derandomization Download PDF
Chapter  47:  Difference Families Download PDF
Chapter  48:  Difference Matrices Download PDF
Chapter  49:  Difference Sets Download PDF
Chapter  50:  Difference Triangle Sets Download PDF
Chapter  51:  Directed Designs Download PDF
Chapter  52:  Factorial Designs Download PDF
Chapter  53:  Frequency Squares and Hypercubes Download PDF
Chapter  54:  Generalized Quadrangles Download PDF
Chapter  55:  Graph Decompositions Download PDF
Chapter  56:  Graph Embeddings and Designs Download PDF
Chapter  57:  Graphical Designs Download PDF
Chapter  58:  Grooming Download PDF
Chapter  59:  Hall Triple Systems Download PDF
Chapter  60:  Howell Designs Download PDF
Chapter  61:  Infinite Designs Download PDF
Chapter  62:  Linear Spaces: Geometric Aspects Download PDF
Chapter  63:  Lotto Designs Download PDF
Chapter  64:  Low Density Parity Check Codes Download PDF
Chapter  65:  Magic Squares Download PDF
Chapter  66:  Mendelsohn Designs Download PDF
Chapter  67:  Nested Designs Download PDF
Chapter  68:  Optimality and Efficiency: Comparing Block Designs Download PDF
Chapter  69:  Ordered Designs, Perpendicular Arrays, and Permutation Sets Download PDF
Chapter  70:  Orthogonal Main Effect Plans Download PDF
Chapter  71:  Packings Download PDF
Chapter  72:  Partial Geometries Download PDF
Chapter  73:  Partially Balanced Incomplete Block Designs Download PDF
Chapter  74:  Perfect Hash Families Download PDF
Chapter  75:  Permutation Codes and Arrays Download PDF
Chapter  76:  Permutation Polynomials Download PDF
Chapter  77:  Pooling Designs Download PDF
Chapter  78:  Quasi-3 Designs Download PDF
Chapter  79:  Quasi-Symmetric Designs Download PDF
Chapter  80:  (r, λ)-designs Download PDF
Chapter  81:  Room Squares Download PDF
Chapter  82:  Scheduling a Tournament Download PDF
Chapter  83:  Secrecy and Authentication Codes Download PDF
Chapter  84:  Skolem and Langford Sequences Download PDF
Chapter  85:  Spherical Designs Download PDF
Chapter  86:  Starters Download PDF
Chapter  87:  Superimposed Codes and Combinatorial Group Testing Download PDF
Chapter  88:  Supersimple Designs Download PDF
Chapter  89:  Threshold and Ramp Schemes Download PDF
Chapter  90:  (t,m,s)-Nets Download PDF
Chapter  91:  Trades Download PDF
Chapter  92:  Turán Systems Download PDF
Chapter  93:  Tuscan Squares Download PDF
Chapter  94:  t-Wise Balanced Designs Download PDF
Chapter  95:  Whist Tournaments Download PDF
Chapter  96:  Youden Squares and Generalized Youden Designs Download PDF
Chapter  97:  Codes Download PDF
Chapter  98:  Finite Geometry Download PDF
Chapter  99:  Divisible Semiplanes Download PDF
Chapter  100:  Graphs and Multigraphs Download PDF
Chapter  101:  Factorizations of Graphs Download PDF
Chapter  102:  Computational Methods in Design Theory Download PDF
Chapter  103:  Linear Algebra and Designs Download PDF
Chapter  104:  Number Theory and Finite Fields Download PDF
Chapter  105:  Finite Groups and Designs Download PDF
Chapter  106:  Designs and Matroids Download PDF
Chapter  107:  Strongly Regular Graphs Download PDF
Chapter  108:  Directed Strongly Regular Graphs Download PDF
Chapter  109:  Two-Graphs Download PDF
Bibliography Download PDF
Index Download PDF
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