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Introduction to the Theory of Matroids (Lecture Notes in Economics and Mathematical Systems, 109) - Softcover
Synopsis
Matroid theory has its origin in a paper by H. Whitney entitled "On the abstract properties of linear dependence" [35], which appeared in 1935. The main objective of the paper was to establish the essential (abstract) properties of the concepts of linear dependence and independence in vector spaces, and to use these for the axiomatic definition of a new algebraic object, namely the matroid. Furthermore, Whitney showed that these axioms are also abstractions of certain graph-theoretic concepts. This is very much in evidence when one considers the basic concepts making up the structure of a matroid: some reflect their linear algebraic origin, while others reflect their graph-theoretic origin. Whitney also studied a number of important examples of matroids. The next major development was brought about in the forties by R. Rado's matroid generalisation of P. Hall's famous "marriage" theorem. This provided new impulses for transversal theory, in which matroids today play an essential role under the name of "independence structures", cf. the treatise on transversal theory by L. Mirsky [26J. At roughly the same time R.P. Dilworth estab lished the connection between matroids and lattice theory. Thus matroids became an essential part of combinatorial mathematics. About ten years later W.T. Tutte [30] developed the funda mentals of matroids in detail from a graph-theoretic point of view, and characterised graphic matroids as well as the larger class of those matroids that are representable over any field.
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- PublisherSpringer
- Publication date1975
- ISBN 10 3540071776
- ISBN 13 9783540071778
- BindingPaperback
- LanguageEnglish
- Number of pages116
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Introduction to the Theory of Matroids Lecture notes in economics and mathematical systems, vol. 109
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Introduction to the theory of matroids.
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Introduction to the Theory of Matroids. Lecture Notes in Economical and Mathematical Systems 109
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Introduction to the theory of matroids. Lecture notes in economics and mathematical systems, 109: Mathemat. economics.
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Introduction to the Theory of Matroids (Lecture Notes in Economics and Mathematical Systems, 109)
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Introduction to the Theory of Matroids (Lecture Notes in Economics and Mathematical Systems, 109)
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Introduction to the Theory of Matroids
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Matroid theory has its origin in a paper by H. Whitney entitled 'On the abstract properties of linear dependence' [35], which appeared in 1935. The main objective of the paper was to establish the essential (abstract) properties of the concepts of linear dependence and independence in vector spaces, and to use these for the axiomatic definition of a new algebraic object, namely the matroid. Furthermore, Whitney showed that these axioms are also abstractions of certain graph-theoretic concepts. This is very much in evidence when one considers the basic concepts making up the structure of a matroid: some reflect their linear algebraic origin, while others reflect their graph-theoretic origin. Whitney also studied a number of important examples of matroids. The next major development was brought about in the forties by R. Rado's matroid generalisation of P. Hall's famous 'marriage' theorem. This provided new impulses for transversal theory, in which matroids today play an essential role under the name of 'independence structures', cf. the treatise on transversal theory by L. Mirsky [26J. At roughly the same time R.P. Dilworth estab lished the connection between matroids and lattice theory. Thus matroids became an essential part of combinatorial mathematics. About ten years later W.T. Tutte [30] developed the funda mentals of matroids in detail from a graph-theoretic point of view, and characterised graphic matroids as well as the larger class of those matroids that are representable over any field. Seller Inventory # 9783540071778
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Introduction to the Theory of Matroids (Lecture Notes in Economics and Mathematical Systems)
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Introduction to the Theory of Matroids
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Matroid theory has its origin in a paper by H. Whitney entitled On the abstract properties of linear dependence [35], which appeared in 1935. The main objective of the paper was to establish the essential (abstract) properties of the concepts of linear de. Seller Inventory # 4879515
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Introduction to the Theory of Matroids
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