Triple Systems [Hardcover]

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.

An 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 triple 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. STSs with two subsystems
22. Nested and derived triple systems
23. Decomposability
24. Directed triple systems
25. Mendelsohn triple systems
Bibliography
Index

This magnificent bible on triple systems should belong on the shelves of everyone who works in triple systems and block designs. It will be a useful reference text for people in allied fields such as graph theory and cryptography. The level of the text is aimed at graduate and research use, although some chapters could be used as a basis for an honours student's project. . . . [J]ustlœ