Combinatorics
Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

Frontispiece, Preface, 1. Notation, 2. Representing sets, 3. Sperner systems, 4. The Littlewood - Offord problem, 5. Shadows, 6. Random sets, 7. Intersecting hypergraphs, 8. The Turán problem, 9. Saturated hypergraphs, 10. Well-separated systems, 11. Helly families, 12. Hypergraphs with a given number of disjoint edges, 13. Intersecting families, 14. Factorizing complete hypergraphs, 15. Weakly saturated hypergraphs, 16. Isoperimetric problems, 17. The trace of a set system, 18. Partitioning sets of vectors, 19. The four functions theorem, 20. Infinite ramsey theory, References, Index.