Lectures on PolytopesSpringer Science & Business Media, 3 mai 2012 - 370 pages Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students. |
Table des matières
Introduction and Examples | 1 |
Polytopes Polyhedra and Cones | 27 |
Faces of Polytopes | 51 |
Graphs of Polytopes | 77 |
Steinitz Theorem for 3Polytopes | 103 |
Schlegel Diagrams for 4Polytopes | 127 |
Duality Gale Diagrams and Applications | 149 |
Fans Arrangements Zonotopes | 191 |
Shellability and the Upper Bound Theorem | 231 |
Fiber Polytopes and Beyond | 291 |
References | 325 |
| 365 | |
Autres éditions - Tout afficher
Lectures on Polytopes (Graduate Texts in Mathematics 152) Günter M. Ziegler Aucun aperçu disponible - 1995 |
Expressions et termes fréquents
affine Algebraic algorithm apply arrangement associated assume basic boundary called circuits combinatorial combinatorially equivalent complex Comput condition cone configuration conjecture connected consider construction contained convex coordinates corresponding cube cyclic d-polytope define Definition denote describe determined dimension Discrete drawing dual edges element equality example Exercise face facets fact figure finite Gale diagram Geometry given graph hyperplane inequalities interior intersection lattice least Lecture Lemma linear function Math Mathematics maximal minimal Minkowski sum multiset Note oriented matroid particular path plane polar polyhedra polytope poset positive problem projection proof properties prove realization refer regular represented respect result satisfies Schlegel diagram Sect shellable shelling Show sign vectors simple simplex simplicial simplicial complex space structure Sturmfels subdivision theorem Theory transformation triangulation unique upper bound vertex vertices zonotope