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

Béla Bollobás (Edited by)

9780521337038, Cambridge University Press

Paperback, published 31 July 1986

192 pages
23.1 x 15.8 x 1.4 cm, 0.29 kg

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.

Subject Areas: Combinatorics & graph theory [PBV]