UID:
edocfu_9959240276002883
Format:
1 online resource (xii, 212 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88425-5
,
1-107-10255-3
,
1-107-08779-1
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1-107-09999-4
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1-107-09404-6
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1-107-32571-4
Series Statement:
Encyclopedia of mathematics and its applications ;
Content:
This book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume begins with three chapters on coordinatisations, followed by one on matching theory. The next two deal with transversal and simplicial matroids. These are followed by studies of the important matroid invariants. The final chapter deals with matroids in combinatorial optimisation, a topic of much current interest. The whole volume has been carefully edited to ensure a uniform style and notation throughout, and to make a work that can be used as a reference or as an introductory textbook for graduate students or non-specialists.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Half Title; Title; Copyright; CONTRIBUTORS; SERIES EDITOR'S STATEMENT; PREFACE; 1 Coordinatizations; 1.1. Introduction and Basic Definitions; 1.2. Equivalence of Coordinatizations and Canonical Forms; 1.3. Matroid Operations; 1.4. Non-coordinatizable Geometries; 1.5. Necessary and Sufficient Conditions for Coordinatization; 1.6. Brackets; 1.7. Coordinatization over Algebraic Extensions; 1.8. Characteristic Sets; 1.9. Coordinatizations over Transcendental Extensions; 1.10. Algebraic Representation; Exercises; References; 2 Binary Matroids; 2.1. Definition and Basic Properties
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2.2. Characterizations of Binary Matroids2.3. Related Characterizations; 2.4. Spaces of Circuits of Binary Matroids; 2.5. Coordinatizing Matrices of Binary Matroids; 2.6. Special Classes of Binary Matroids; Graphic Matroids; 2.7. Appendix on Modular Pairs of Circuits in a Matroid; Exercises; References; 3 Unimodular Matroids; 3.1. Equivalent Conditions for Unimodularity; 3.2. Tutte's Homotopy Theorem and Excluded Minor Characterization; 3.3. Applications of unimodularity; Exercises; References; 4 Introduction to Matching Theory; 4.1. Matchings on Matroids; 4.2. Matching Matroids
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4.3. ApplicationsNotes; Exercises; References; 5 Transversal Matroids; 5.1. Introduction; 5.2. Presentations; 5.3. Duals of Transversal Matroids; 5.4. Other Properties and Generalizations; Notes; Exercises; References; 6 Simplicial Matroids; 6.1. Introduction; 6.2. Orthogonal Full Simplicial Matroids; 6.3. Binary and Unimodular Full Simplicial Geometries; 6.4. Uniquely Coordinatizable Full Simplicial Matroids; 6.5. Matroids on the Bases of Matroids; 6.6. Sperner's Lemma for Geometries; 6.7. Other Results; Exercises; References; 7 The Mobius Function and the Characteristic Polynomial
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7.1. The Mobius Function7.2. The characteristic Polynomial; 7.3. The beta Invariant; 7.4. Tutte-Grothendieck Invariance; 7.5. Examples; 7.6. The Critical Problem; Exercises; References; 8 Whitney Numbers; 8.1. Introduction; 8.2. The Characteristic and Rank Polynomials; 8.3. The Mobius Algebra; 8.4. The Whitney Numbers of the First Kind; 8.5. The Whitney Numbers of the Second Kind; 8.6. Comments; References; 9 Matroids in Combinatorial Optimization; 9.1. The Greedy Algorithm and Matroid Polyhedra; 9.2. Intersections and Unions of Matroids; 9.3. Integral Matroids; 9.4. Submodular Systems
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9.5. Submodular FlowsExercises; References; INDEX
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English
Additional Edition:
ISBN 0-521-07036-8
Additional Edition:
ISBN 0-521-33339-3
Language:
English
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