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Triangulations : structures for algorithms and applications
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| Auteurs principaux : | , , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Triangulations : structures for algorithms and applications / Jesús A. De Loera, Jörg Rambau, Francisco Santos |
| Publié : |
Heidelberg, London, New York [etc.] :
Springer
, C 2010 |
| Description matérielle : | 1 vol. (XIII-535 p.) |
| Collection : | Algorithms and computation in mathematics ; 25 |
| Contenu : | Contient des exercices |
| Sujets : | |
| Documents associés : | Autre format:
Triangulations |
- 1 Triangulations in Mathematics
- 1.1 Combinatorics and triangulations
- 1.2 Optimization and triangulations
- 1.3 Algebra and triangulations
- 1.4 The rest of this book
- 2 Configurations, Triangulations, Subdivisions, and Flips
- 2.1 The official languages in the land of triangulations
- 2.2 A closer look at the definition of triangulations
- 2.3 A bullet-proof definition of polyhedral subdivisions
- 2.4 Flips and the graph of triangulations
- 2.5 Vector configurations and their triangulations
- 2.6 Triangulations as simplicial complexes
- 3 Life in Two Dimensions
- 3.1 Some basic properties
- 3.2 A few examples of triangulations in the plane
- 3.3 The set of all triangulations of a point set
- 3.4 Flips in triangulations
- 3.5 Pseudo-triangulations
- 3.6 Life in three dimensions
- 3.7 Notes and References
- 4 A Tool Box
- 4.1 Combinatorics of configurations
- 4.2 Manipulating vector configurations
- 4.3 Generating polyhedral subdivisions
- 4.4 Two equivalent characterizations of flips
- 5 Regular Triangulations and Secondary Polytopes
- 5.1 The secondary polytope
- 5.2 The normal fan of the secondary polytope
- 5.3 Structure of the secondary polytope
- 5.4 Chambers
- 5.5 Configurations with fixed corank
- 6 Some Interesting Configurations
- 6.1 Cyclic polytopes
- 6.2 Products of two simplices
- 6.3 Cubes and their subpolytopes
- 7 Some Interesting Triangulations
- 7.1 The mother of all examples, and some relatives
- 7.2 Highly flip-deficient triangulations
- 7.3 Dimension 5: A disconnected graph of triangulations with unimodular triangulations
- 8 Algorithmic Issues
- 8.1 Tools for computation
- 8.2 Verification and realizability
- 8.3 Listing and enumerating triangulations
- 8.4 Bounding the number of triangulations
- 8.5 Optimization
- 8.6 Computational complexity of triangulation problems
- 9 Further Topics
- 9.1 Fiber polytopes
- 9.2 Mixed subdivisions and the Cayley trick
- 9.3 Lattice polytopes and unimodular triangulations
- 9.4 Triangulations and Gröbner bases
- 9.5 Polytopal complexes and regular triangulations