Lectures on Polytopes.
- These lecture notes have several aims: \begin{itemize} \item to give an introduction to some basic facts about convex polytopes, with an emphasis on the basic methods that yield them (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms and oriented matroids), \item to discuss some important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associahedra, fiber polytopes, the Lawrence construction) \item and to illustrate why polytope theory is exciting, with highlights like Kalai's new diameter bounds, the construction of non-rational polytopes, the Bohne-Dress tiling theorem, shellability and the upper bound theorem, .... \end{itemize} For several of these topics the decisive break-through is very recent, which suggests that there is much more discovered.
| Author: | Günter M. Ziegler |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1993/05/28 |
| Series (Serial Number): | ZIB-Report (TR-93-06) |
| ZIB-Reportnumber: | TR-93-06 |
| Notes: | No preprint available; published as Ziegler, G. M. (1994) Lectures on Polytopes. ISBN 354094365X, New York: Springer |
| Published in: | Published as Ziegler, G. M. (1994) Lectures on Polytopes. ISBN 354094365X, New York: Springer |
