Sperner theory
著者
書誌事項
Sperner theory
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 65）
Cambridge University Press, 1997
大学図書館所蔵 全86件
注記
Bibliography: p. 395-412
Includes index
内容説明・目次
内容説明
The starting point of this book is Sperner's theorem, which answers the question: What is the maximum possible size of a family of pairwise (with respect to inclusion) subsets of a finite set? This theorem stimulated the development of a fast growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics. Researchers and graduate students in discrete mathematics, optimisation, algebra, probability theory, number theory, and geometry will find many powerful new methods arising from Sperner theory.
目次
- 1. Introduction
- 2. Extremal problems for finite sets
- 3. Profile-polytopes
- 4. The flow-theoretic approach
- 5. Symmetric chain orders
- 6. Algebraic methods in Sperner theory
- 7. Limit theorems
- 8. Macaulay posets.
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