Triple Systems by Charles Colbourn

Triple Systems

byCharles Colbourn, Alex Rosa

Hardcover | March 1, 1999

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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. Triplesystems 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 anextensive, 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 techniqueare included, as is a comprehensive bibliography.

About The Author

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

Details & Specs

Title:Triple SystemsFormat:HardcoverPublished:March 1, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198535767

ISBN - 13:9780198535768

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Table of Contents

Historical introduction1. Design-theoretic fundamentals2. Existence: direct methods3. Existence:recursive methods4. Isomorphism and invariants5. Enumeration6. Subsystems and holes7. Automorphisms I: small groups8. Automorphisms II: large groups9. Leaves and partial tripls systems10. Excesses and coverings11. Embedding and its variants12. Neighbourhoods13. Configurations14. Intersections15. Large sets and partitions16. Support sizes17. Independent sets18. Chromatic number19. Chromatic index and resolvability20. Orthogonal resolutions21. Nested and derived triple systems22. Decomposability23. Directed triple systems24. Mendelsohn triple systemsBibliographiesIndex