Combinatorics of Finite Sets Book

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.Read More