Triple systems
著者
書誌事項
Triple systems
（Oxford mathematical monographs）
Clarendon Press, 1999
- : hbk
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注記
Includes bibliographical references (p. [457]-549) and index
内容説明・目次
内容説明
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.
目次
- 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
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