Introduction to the Theory of Matroids:
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 vect...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1975
|
| Ausgabe: | 1st ed. 1975 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
109 |
| Schlagworte: | |
| Online-Zugang: | BTU01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (X, 106 p. 2 illus) |
| ISBN: | 9783642482922 |
| DOI: | 10.1007/978-3-642-48292-2 |
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| 520 | |a 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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| edition | 1st ed. 1975 |
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| spelling | Randow, R. v Verfasser aut Introduction to the Theory of Matroids by R. v. Randow 1st ed. 1975 Berlin, Heidelberg Springer Berlin Heidelberg 1975 1 Online-Ressource (X, 106 p. 2 illus) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 109 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 Economic Theory/Quantitative Economics/Mathematical Methods Mathematics, general Economic theory Mathematics Theorie (DE-588)4059787-8 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Matroid (DE-588)4128705-8 gnd rswk-swf Matroid (DE-588)4128705-8 s Theorie (DE-588)4059787-8 s DE-604 Graphentheorie (DE-588)4113782-6 s Erscheint auch als Druck-Ausgabe 9783540071778 Erscheint auch als Druck-Ausgabe 9783642482939 https://doi.org/10.1007/978-3-642-48292-2 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Randow, R. v Introduction to the Theory of Matroids Economic Theory/Quantitative Economics/Mathematical Methods Mathematics, general Economic theory Mathematics Theorie (DE-588)4059787-8 gnd Graphentheorie (DE-588)4113782-6 gnd Matroid (DE-588)4128705-8 gnd |
| subject_GND | (DE-588)4059787-8 (DE-588)4113782-6 (DE-588)4128705-8 |
| title | Introduction to the Theory of Matroids |
| title_auth | Introduction to the Theory of Matroids |
| title_exact_search | Introduction to the Theory of Matroids |
| title_exact_search_txtP | Introduction to the Theory of Matroids |
| title_full | Introduction to the Theory of Matroids by R. v. Randow |
| title_fullStr | Introduction to the Theory of Matroids by R. v. Randow |
| title_full_unstemmed | Introduction to the Theory of Matroids by R. v. Randow |
| title_short | Introduction to the Theory of Matroids |
| title_sort | introduction to the theory of matroids |
| topic | Economic Theory/Quantitative Economics/Mathematical Methods Mathematics, general Economic theory Mathematics Theorie (DE-588)4059787-8 gnd Graphentheorie (DE-588)4113782-6 gnd Matroid (DE-588)4128705-8 gnd |
| topic_facet | Economic Theory/Quantitative Economics/Mathematical Methods Mathematics, general Economic theory Mathematics Theorie Graphentheorie Matroid |
| url | https://doi.org/10.1007/978-3-642-48292-2 |
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