The combinatorial study of finite set systems is a lively area of research unified by the gradual discovery of structural insights and widely applicable proof techniques. This book is the first coherent and up-to-date account of the basic methods and results of this study. Much of the material in the book concerns subsets of a set, but chapters also cover more general partially ordered sets. For example, the Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is discussed, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are presented. Each chapter ends with a collection of exercises for which outline solutions are provided, and there is an extensive bibliography. The work is important for postgraduate students and researchers in discrete mathematics and related subjects.
- ISBN10 0198533675
- ISBN13 9780198533672
- Publish Date 5 February 1987
- Publish Status Out of Print
- Out of Print 2 June 2000
- Publish Country GB
- Publisher Oxford University Press
- Imprint Clarendon Press
- Format Hardcover
- Pages 264
- Language English