Description
Book SynopsisTriple systems are among the simplest combinatorial designs. They have applications in coding theory, cryptography, computer science, statistcs, and many other areas. This book provides the first systematic and comprehensive treatment of triple systems. It gives an accurate picture of an incredibly rich and vibrant area of combinatorial mathematics.
Table of ContentsHistorical 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
