Triangulations of Oriented Matroids.
Santos, Francisco.
Triangulations of Oriented Matroids. - 1st ed. - 1 online resource (95 pages) - Memoirs of the American Mathematical Society ; v.156 . - Memoirs of the American Mathematical Society .
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.
9781470403348
Oriented matroids.
Polytopes.
Triangularization (Mathematics).
Electronic books.
QA166.6 -- .S26 2002eb
510 s;511/.6
Triangulations of Oriented Matroids. - 1st ed. - 1 online resource (95 pages) - Memoirs of the American Mathematical Society ; v.156 . - Memoirs of the American Mathematical Society .
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.
9781470403348
Oriented matroids.
Polytopes.
Triangularization (Mathematics).
Electronic books.
QA166.6 -- .S26 2002eb
510 s;511/.6