The Resource Combinatorial geometries, edited by Neil White, (electronic resource)

Combinatorial geometries, edited by Neil White, (electronic resource)

Label
Combinatorial geometries
Title
Combinatorial geometries
Statement of responsibility
edited by Neil White
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
This book is a continuation of Theory of Matroids and again consists of a series of related surveys
Member of
Cataloging source
MiAaPQ
Dewey number
  • 516.13
  • 516/.13
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA166.6
LC item number
.C66 1987
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1945-
http://library.link/vocab/relatedWorkOrContributorName
White, Neil
Series statement
  • Encyclopedia of mathematics and its applications
  • Encyclopedia of Mathematics and its Applications
Series volume
  • v. 29
  • v.29
http://library.link/vocab/subjectName
  • Matroids
  • Combinatorial geometry
Label
Combinatorial geometries, edited by Neil White, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographies and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • 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
  • 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
  • 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
  • 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
  • 9.5. Submodular FlowsExercises; References; INDEX
Dimensions
unknown
Extent
1 online resource (226 p.)
Form of item
online
Isbn
9781139884259
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000356573
  • (EBL)1179182
  • (SSID)ssj0000877416
  • (PQKBManifestationID)11446564
  • (PQKBTitleCode)TC0000877416
  • (PQKBWorkID)10907748
  • (PQKB)10962045
  • (UkCbUP)CR9781107325715
  • (MiAaPQ)EBC1179182
  • (EXLCZ)992670000000356573
Label
Combinatorial geometries, edited by Neil White, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographies and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • 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
  • 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
  • 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
  • 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
  • 9.5. Submodular FlowsExercises; References; INDEX
Dimensions
unknown
Extent
1 online resource (226 p.)
Form of item
online
Isbn
9781139884259
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000356573
  • (EBL)1179182
  • (SSID)ssj0000877416
  • (PQKBManifestationID)11446564
  • (PQKBTitleCode)TC0000877416
  • (PQKBWorkID)10907748
  • (PQKB)10962045
  • (UkCbUP)CR9781107325715
  • (MiAaPQ)EBC1179182
  • (EXLCZ)992670000000356573

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