Handbook of Combinatorial Designs

Front Cover
Charles J. Colbourn, Jeffrey H. Dinitz
CRC Press, Nov 2, 2006 - Computers - 1016 pages
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
 

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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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