Triple Systems

Portada
Among the simplest combinatorial designs, triple systems are a natural generalization of graphs and have connections with geometry, algebra, group theory, finite fields, and cyclotomy. Applications of triple systems are found in coding theory, cryptography, computer science, and statistics. In
many cases, triple systems provide the prototype for deep results in combinatorial design theory, and a number of important results were first understood in the context of triple systems and then generalized. This book attempts to survey current knowledge on the subject, to gather together common
themes, and to provide an accurate portrait of the huge variety of problems and results. It includes representative samples of the major styles of proof technique and a comprehensive bibliography.
 

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Continguts

An historical introduction
1
Designtheoretic fundamentals
13
Independent sets
17
direct methods
23
recursive methods
39
Isomorphism and invariants
49
Enumeration
61
Subsystems and holes
77
Configurations
209
Intersections
247
Large sets and partitions
267
Support sizes
279
Orthogonal resolutions
373
STSs with two subsystems
381
Nested and derived triple systems
399
Decomposability
410

small groups
101
large groups
141
Leaves and partial triple systems
155
Excesses and coverings
177
Embedding and its variants
185
Neighbourhoods
199
Directed triple systems
422
Mendelsohn triple systems
442
Bibliography
457
Index
551
Copyright

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Sobre l'autor (1999)

Charles Colbourn is at University of Vermont. Alex Rosa is at McMaster University.

Informació bibliogràfica