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Technical Semimodular Lattices: Theory and Applications (Encyclopedia of Mathe

Posted on 2010-08-11




Name:Technical Semimodular Lattices: Theory and Applications (Encyclopedia of Mathe
ASIN/ISBN:0521461057
Publish Date:1999
Pages:388 pages
File size:10 Mb
Publish Date: 1999
ISBN: 0521461057
Pages: 388 pages
File Type: PDF
File Size: 10 MB
Other Info: Cambridge University Press
   Technical Semimodular Lattices: Theory and Applications (Encyclopedia of Mathe

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Manfred Stern, "Semimodular Lattices: Theory and Applications (Encyclopedia of Mathe"

Lattice theory evolved as part of algebra in the nineteenth century through the work of Boole, Peirce and Schröder, and in the first half of the twentieth century through the work of Dedekind, Birkhoff, Ore, von Neumann, Mac Lane, Wilcox, Dilworth, and others. In Semimodular Lattices, 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 author surveys and analyzes Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and he presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. Special emphasis is given to the combinatorial aspects of finite semimodular lattices and to the connections between matroids and geometric lattices, antimatroids and locally distributive lattices. The book also deals with lattices that are "close" to semimodularity or can be combined with semimodularity, for example supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book valuable.

• Introduces the theory of semimodular lattices as a far-reaching generalization of Boolean algebras • Examines the interdependence of related concepts such as M-symmetry and conditions of MacLane and Dilworth • Has applications to discrete mathematics, combinatorics, group theory and universal algebra

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