Semimodular lattices : theory and applications
著者
書誌事項
Semimodular lattices : theory and applications
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 73）
Cambridge University Press, 1999
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.
目次
- Preface
- 1. From Boolean algebras to semimodular lattices
- 2. M-symmetric lattices
- 3. Conditions related to semimodularity, 0-conditions and disjointness properties
- 4. Supersolvable and admissible lattices, consistent and strong lattices
- 5. The covering graph
- 6. Semimodular lattices of finite length
- 7. Local distributivity
- 8. Local modularity
- 9. Congruence semimodularity
- Master reference list
- Table of notation
- Index.
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