Combination of Finite Sets

Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, 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 also discussed.