Combinatorics of Finite Sets

by Anderson, Ian

• ISBN13: 9780198533795
• ISBN10: 0198533799
• Format: Paperback
• Copyright: 1989-05-18
• Publisher: Oxford University Press

Summary

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.

Table of Contents

Introduction and Sperner's Theorem

Normalized Matchings and Rank Numbers

Symmetric Chains

Rank Numbers for Multisets

Intersecting Systems and the Erdos-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

Table of Contents provided by Publisher. All Rights Reserved.