Contemporary design theory: a collection of surveys
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York u.a.
Wiley
1992
|
| Series: | Wiley-Interscience series in discrete mathematics and optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 639 S. |
| ISBN: | 0471531413 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804120682204758016 |
|---|---|
| adam_text | Contents
Preface xv
1 A Brief Introduction to Design Theory 1
Jeffrey H. Dinitz and Douglas R. Stinson
1 Balanced Incomplete Block Designs 1
2 r Designs 4
3 Automorphisms and Isomorphisms of Designs 6
4 Pairwise Balanced Designs 6
5 Latin Squares 9
6 Graphs 10
7 Remarks 12
References 12
2 Orthogonal Factorizations of Graphs 13
Brian Alspach, Katherine Heinrich, and Guizhen Liu
1 Introduction 13
2 1 Factorizations 15
3 Matching Factorizations 21
4 Other Types of Orthogonal and Suborthogonal
Factorizations 25
5 Self Orthogonality and Applications 32
6 Open Problems 36
References 37
3 Conjugate Orthogonal Latin Squares and Related Structures 41
F. E. Bennett and L. Zhu
1 Introduction 41
2 Some Fundamental Constructions 45
ix
x Contents
3 COILS and Related Structures 47
4 Latin Squares with Pairwise Orthogonal Conjugates 54
5 Conjugate Orthogonal Latin Square Graphs 59
6 Pairwise Orthogonal Conjugate Latin Squares 62
7 Conjugate Orthogonal Quasigroup Identities and Related
Designs 64
8 Incomplete COILS 77
9 COLS with Holes 84
10 Open Problems 88
References 90
4 Directed and Mendelsohn Triple Systems 97
Charles J. Colbourn and Alexander Rosa
1 Directed Triple Systems 97
2 Mendelsohn Triple Systems 116
3 Hybrid Triple Systems 128
4 Other Species 130
5 Open Problems 131
References 132
5 Room Squares and Related Designs 137
Jeffrey H. Dinitz and Douglas R. Stinson
1 Introduction and History 137
2 Direct Constructions 141
3 Room Frames 152
4 Room Squares with Subsquares 159
5 Room d Cubes of Dimension Exceeding Two 163
6 Nonisomorphic Room Squares 165
7 Skew Room Squares 167
8 Perfect Room Squares 170
9 Maximum Empty Suba rray Room Squares 172
10 Balanced Howell Rotations 173
11 Howell Designs 176
12 Orthogonal Steiner Triple Systems 182
13 Orthogonal Edge Colorings of Graphs 184
14 Houses 186
15 Orthogonal One Factorization Graphs 187
16 Balanced Tournament Designs 189
Contents xi
17 Other Generalizations 191
18 Open Problems 191
References 194
6 Steiner Quadruple Systems 205
Alan Hartman and Kevin T. Phelps
1 Construction 205
2 Isomorphism 211
3 Automorphism Groups 213
4 Coloring 216
5 Intersection Problems 218
6 Derived Triple Systems 221
7 Embedding 222
8 Resolvability 223
9 Packing and Covering 227
10 Ordered Quadruple Systems and 3 Quasigroups 228
11 Higher Lambda 230
12 Open Problems 232
References 236
7 Difference Sets 241
Dieter Jungnickel
1 Difference Sets and Symmetric Designs 242
2 Multipliers 245
3 Group Rings and Characters 248
4 Multiplier Theorems 252
5 Wilbrink s Theorem 256
6 Difference Lists 259
7 The Mann Test and Its Variations 263
8 Planar Difference Sets 268
9 Hadamard Difference Sets 274
10 Cyclotomy and Difference Sets 276
11 The Construction of McFarland and Its Variations 280
12 Menon Difference Sets 282
13 Difference Sets with Multiplier 1 288
14 The Structure of Sylow Subgroups 291
15 Difference Sets and Codes 296
16 Difference Sets and Finite Geometries 303
17 Open Problems 309
xii Contents
Appendix: A Table of Abelian Difference Sets of Order
n 30 311
References 317
8 Decomposition into Cycles II: Cycle Systems 325
C. C. Lindner and C. A. Rodger
1 Introduction 325
2 Existence of m Cycle Systems 326
3 Two Perfect m Cycle Systems 334
4 Resolvability 345
5 Nesting 354
6 Embedding Theorems 358
7 Open Problems 364
References 365
9 Coverings and Packings 371
W. H. Mills and R. C. Midlin
1 Introduction 371
2 Covering Bounds 375
3 Coverings for k and t Fixed 377
4 Covering Results for a Fixed Number of Blocks 380
5 Miscellaneous Covering Results for Small v and A = 1 381
6 Packing Bounds 384
7 Packings with k and t Fixed 385
8 Miscellaneous Packing Results for Small v and A = 1 386
9 Results from Finite Geometries and Finite Fields 389
10 Related Covering and Packing Problems 390
11 Isomorphism of Covering Designs 393
12 Asymptotic Results 394
13 Algorithms for Covering and Packing Designs 394
14 Open Problems 394
References 395
10 Colorings of Block Designs 401
Alexander Rosa and Charles J. Colbourn
1 Independent Sets in Designs 402
2 Coloring Elements and the Chromatic Number 405
3 Coloring Blocks and the Chromatic Index 415
Contents xiii
4 Coloring Algorithms and Complexity of Coloring Block
Designs 420
5 Miscellanea: Other Colorings, Related Problems, and
Applications 422
6 Open Problems 424
References 425
11 Hadamard Matrices, Sequences, and Block Designs 431
Jennifer Seberry and Mieko Yamada
1 Introduction 431
2 Hadamard Matrices 437
3 The Strongest Hadamard Construction Theorems 443
4 Orthogonal Designs and Asymptotic Existence 458
5 Sequences 466
6 Amicable Hadamard Matrices and AOD 487
7 Constructions for Skew Hadamard Matrices 492
8 M Structures 498
9 Williamson and Williamson Type Matrices 511
10 SBIBD and the Excess of Hadamard Matrices 523
11 Complex Hadamard Matrices 529
Appendix 535
References 554
12 Large Sets of Disjoint Designs and Related Structures 561
Luc Teirlinck
1 The Existence Problem for Large Sets of Disjoint Designs 561
2 Orthogonal Arrays and Transversal Designs 564
3 Ordered Designs and Perpendicular Arrays 567
4 Generalizations 585
5 Open Problems 587
Appendix 587
References 589
13 One Factorizations of Complete Graphs 593
W. D. Wallis
1 Introduction 593
2 Factors and Factorizations 594
3 Some One Factorizations of Kin 598
xiv Contents
4 One Factorizations of Other Graphs 604
5 Factorizations of Products 606
6 Isomorphisms and Automorphisms 607
7 The Number of One Factorizations 609
8 Tightness and Perfection 612
9 Maximal and Premature Sets 615
10 Applications of One Factorizations I: Tournaments 617
11 Applications of One Factorizations II: Block Designs 619
12 Generalizations and Extensions 620
13 Open Problems 623
Appendix: Starters in Small Groups 624
References 625
Index 633
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| language | English |
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| spelling | Contemporary design theory a collection of surveys ed. by Jeffrey H. Dinitz ... New York u.a. Wiley 1992 XVI, 639 S. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization Kombinatorische Designtheorie (DE-588)4164747-6 gnd rswk-swf Kombinatorische Designtheorie (DE-588)4164747-6 s DE-604 Dinitz, Jeffrey H. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004075835&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Contemporary design theory a collection of surveys Kombinatorische Designtheorie (DE-588)4164747-6 gnd |
| subject_GND | (DE-588)4164747-6 |
| title | Contemporary design theory a collection of surveys |
| title_auth | Contemporary design theory a collection of surveys |
| title_exact_search | Contemporary design theory a collection of surveys |
| title_full | Contemporary design theory a collection of surveys ed. by Jeffrey H. Dinitz ... |
| title_fullStr | Contemporary design theory a collection of surveys ed. by Jeffrey H. Dinitz ... |
| title_full_unstemmed | Contemporary design theory a collection of surveys ed. by Jeffrey H. Dinitz ... |
| title_short | Contemporary design theory |
| title_sort | contemporary design theory a collection of surveys |
| title_sub | a collection of surveys |
| topic | Kombinatorische Designtheorie (DE-588)4164747-6 gnd |
| topic_facet | Kombinatorische Designtheorie |
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