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Theory of Matroids

Author: Neil White
Publisher: Cambridge : Cambridge University Press, 1986.
Series: Encyclopedia of mathematics and its applications, no. 26.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Neil White
ISBN: 9780511629563 0511629567 9780521309370 0521309379 9781107093904 1107093902
OCLC Number: 776957067
Notes: Title from publishers bibliographic system (viewed 22 Dec 2011).
Description: 1 online resource (340 pages).
Contents: Cover --
Half-title --
Title --
Copyright --
Contents --
List of Contributors --
Series Editor's Statement --
Foreword --
Preface --
Chapter 1 Examples and Basic Concepts Henry Crapo --
1.1 Examples from Linear Algebra and Projective Geometry --
1.1.A. Subsets of Projective Spaces --
l.l.B. Vector Geometries --
l.l.C. Function-Space Geometries --
1.2 Further Algebraic Examples --
1.2.A. Examples from Exterior Algebra --
I.2.B. Algebraic Dependence --
1.2.1. Proposition. --
1.3 Combinatorial Examples --
I.3.A. Partitions --
I.3.B. Graphic Geometries --
I.3.C. Simplicial Geometries. I.3.D. Transversal Geometries --
I.3.E. A Geometry of Triples --
I.3.F. Small Geometries --
I.3.G. Coverings --
1.3.1. Proposition --
1.3.2. Proposition --
1.4 Structure and Related Geometries --
1.4.A. Structure Geometries --
I.4.B. Concurrence Geometries --
Exercises --
Chapter 2 Axiom Systems Giorgio Nicoletti and Neil White --
2.1 Basis Axioms --
2.1.1. Proposition --
2.1.2. Corollary --
2.1.3. Proposition --
2.1.4. Proposition --
2.2 Other Families of Subsets --
2.2.1. Proposition --
2.2.2. Corollary --
2.2.3. Proposition --
2.2.4. Proposition --
2.2.5. Proposition --
2.2.6. Theorem. 2.3 Closure and Rank --
2.3.1. Proposition --
2.3.2. Proposition --
2.4 Combinatorial Geometries and Infinite Matroids --
2.4.1. Proposition --
2.4.2. Proposition --
Exercises --
References --
Chapter 3 Lattices Ulrich Faigle --
3.1 Posets and Lattices --
3.1.1. Proposition --
3.1.2. Theorem --
3.2 Modularity --
3.2.1. Proposition --
3.2.2. Theorem --
3.2.3. Proposition --
3.3 Semimodular Lattices of Finite Length --
3.3.1. Theorem --
3.3.2. Theorem --
3.3.3. Theorem --
3.3.4. Corollary --
3.3.5. Corollary --
3.4 Geometric Lattices --
3.4.1. Theorem --
3.4.2. Proposition --
3.4.3. Proposition. 3.4.4. Proposition --
3.4.5. Proposition --
3.4.6. Proposition --
3.5 Decomposition of Geometric Lattices --
3.5.1. Proposition --
3.5.2. Theorem --
3 .5.5. Corollary --
3.6 Projective Geometry and Modular Geometric Lattices --
3.6.1. Lemma --
3.6.2. Theorem --
3.6.3. Corollary --
3.6.4. Theorem --
3.6.5. Corollary --
Exercises --
References --
Chapter 4 Basis-Exchange Properties Joseph P. S. Kung --
4.1 Bracket Identities and Basis-Exchange Properties --
4.1.1. Proposition --
4.1.2. Lemma --
4.2 The Exchange Graph --
4.2.1. Lemma --
4.2.2. Lemma --
4.3 Multiple and Alternating Exchanges. 43.1. Theorem --
4.3.2. Corollary --
4.3.3. Theorem --
4.3.4. Proposition --
Historical Notes --
Exercises --
References --
Chapter 5 Orthogonality Henry Crapo --
5.1 Introduction --
5.2 Orthogonal Geometries --
5.2.1. Theorem --
5.2.2. Proposition --
5.2.3. Proposition --
5.2.4. Proposition --
5.2.5. Proposition --
5.2.6. Theorem --
5.3 Vector Geometries and Function-Space Geometries --
5.3.1. Proposition --
5.3.2. Proposition --
5.3.3 . Proposition --
5.4 Orthogonality of Vector Geometries --
5.4.1. Proposition --
5.4.2. Proposition --
5.4.3. Proposition --
5.4.4. Proposition.
Series Title: Encyclopedia of mathematics and its applications, no. 26.
Responsibility: edited by Neil White.

Abstract:

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial  Read more...

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