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Klappentext 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. Zusammenfassung Triple systems are among the simplest combinatorial designs, and are a natural generalization of graphs. They have connections with geometry, algebra, group theory, finite fields, and cyclotomy; they have applications in coding theory, cryptography, computer science, and statistics. Triple systems provide in many cases the prototype for deep results in combinatorial design theory; this design theory is permeated by problems that were first understood in the context of triple systems and then generalized. Such a rich set of connections has made the study of triple systems an extensive, but sometimes disjointed, field of combinatorics. 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. Representative samples of the major syles of proof technique are included, as is a comprehensive bibliography. Inhaltsverzeichnis Historical introduction 1: Design-theoretic fundamentals 2: Existence: direct methods 3: Existence:recursive methods 4: Isomorphism and invariants 5: Enumeration 6: Subsystems and holes 7: Automorphisms I: small groups 8: Automorphisms II: large groups 9: Leaves and partial tripls systems 10: Excesses and coverings 11: Embedding and its variants 12: Neighbourhoods 13: Configurations 14: Intersections 15: Large sets and partitions 16: Support sizes 17: Independent sets 18: Chromatic number 19: Chromatic index and resolvability 20: Orthogonal resolutions 21: Nested and derived triple systems 22: Decomposability 23: Directed triple systems 24: Mendelsohn triple systems Bibliographies Index ...
