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Triangulations of Oriented Matroids.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2002Copyright date: ©2002Edition: 1st edDescription: 1 online resource (95 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470403348
Subject(s): Genre/Form: Additional physical formats: Print version:: Triangulations of Oriented MatroidsDDC classification:
  • 510 s;511/.6
LOC classification:
  • QA166.6 -- .S26 2002eb
Online resources:
Contents:
Intro -- Contents -- Introduction -- Chapter 1. Preliminaries on Oriented Matroids -- 1.1. Convexity -- 1.2. Extensions. Lexicographic extensions -- 1.3. Euclideanness -- Chapter 2. Triangulations of Oriented Matroids -- 2.1. Definition, characterizations and remarks -- 2.2. Equivalence of the different characterizations -- 2.3. Some properties of triangulations -- 2.4. Topology of triangulations -- Chapter 3. Duality between Triangulations and Extensions -- 3.1. Circuit, cocircuit, extension and triangulation vectors -- 3.2. The affine span of characteristic vectors of triangulations -- 3.3. Mutations versus geometric bistellar flips -- Chapter 4. Subdivisions of Lawrence Polytopes -- 4.1. Lifting subdivisions. Subdivisions -- 4.2. Lawrence polytopes only have lifting subdivisions -- 4.3. The extension space conjecture and the Baues problem -- 4.4. A reoriented Lawrence construction -- Chapter 5. Lifting Triangulations -- 5.1. Some properties. Lifting versus regular triangulations -- 5.2. Three interesting non-lifting triangulations -- 5.3. Two characterizations of lifting subdivisions -- Bibliography.
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Intro -- Contents -- Introduction -- Chapter 1. Preliminaries on Oriented Matroids -- 1.1. Convexity -- 1.2. Extensions. Lexicographic extensions -- 1.3. Euclideanness -- Chapter 2. Triangulations of Oriented Matroids -- 2.1. Definition, characterizations and remarks -- 2.2. Equivalence of the different characterizations -- 2.3. Some properties of triangulations -- 2.4. Topology of triangulations -- Chapter 3. Duality between Triangulations and Extensions -- 3.1. Circuit, cocircuit, extension and triangulation vectors -- 3.2. The affine span of characteristic vectors of triangulations -- 3.3. Mutations versus geometric bistellar flips -- Chapter 4. Subdivisions of Lawrence Polytopes -- 4.1. Lifting subdivisions. Subdivisions -- 4.2. Lawrence polytopes only have lifting subdivisions -- 4.3. The extension space conjecture and the Baues problem -- 4.4. A reoriented Lawrence construction -- Chapter 5. Lifting Triangulations -- 5.1. Some properties. Lifting versus regular triangulations -- 5.2. Three interesting non-lifting triangulations -- 5.3. Two characterizations of lifting subdivisions -- Bibliography.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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