Combinatorics of finite sets
著者
書誌事項
Combinatorics of finite sets
（Oxford science publications）
Clarendon Press, 1989, c1987
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注記
Bibliography: p. 241-248
Includes index
内容説明・目次
内容説明
It is the aim of this book to provide a coherent and up-to-date account of the basic methods and results of the combinatorial study of finite set systems. From its origins in a 1928 theorem of Sperner, this subject has become a lively area of combinatorial research, unified by the gradual discovery of structural insights and widely applicable proof techniques. Much of the material in the book concerns subsets of a set, but there are chapters dealing with more general partially ordered sets: for example, the Clements-Lindstr on extension of the Kruscal-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.
目次
- Introduction and Sperner's theorem
- Normalized matchings and rank numbers
- Symmetric chains
- Rank numbers for multisets
- Intersecting systems and the Erd "os-Ko-Rado theorem
- Ideals and a lemma of Kleitman
- The Kruskal-Katona theorem
- Antichains
- The generalized Macaulay theorem for multisets
- Theorems for multisets
- The Littlewood-Offord problem
- Miscellaneous methods
- Lattices of antichains and saturated chain partitions
- Hints and solutions.
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