Combinatorics of Finite Sets 1st Edition by Ian Anderson ISBN 0486422577 9780486422572

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Product details:

ISBN 10: 0486422577

ISBN 13: 9780486422572

Author: Ian Anderson 

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. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. “An excellent text for a topics course in discrete mathematics.” — Bulletin of the American Mathematical Society.

Table of contents:

Chapter 1: Introduction and Sperner’s Theorem
Chapter 2: Normalized Matchings and Rank Numbers
Chapter 3: Symmetric Chains
Chapter 4: Rank Numbers for Multisets
Chapter 5: Intersecting Systems and the Erdös-Ko-Rado Theorem
Chapter 6: Ideals and a Lemma of Kleitman
Chapter 7: The Kruskal-Katona Theorem
Chapter 8: Antichains
Chapter 9: The Generalized Macaulay Theorem for Multisets
Chapter 10: Theorems for Multisets
Chapter 11: The Littlewood-Offord Problem
Chapter 12: Miscellaneous Methods
Chapter 13: Lattices of Antichains and Saturated Chain Partitions

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Tags: Ian Anderson, Combinatorics, Finite Sets