# Lectures on Polytopes

@inproceedings{Ziegler1994LecturesOP, title={Lectures on Polytopes}, author={G{\"u}nter M. Ziegler}, year={1994} }

Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions. The lectures - introduce the basic facts…

## 3,254 Citations

Topics in algorithmic, enumerative and geometric combinatorics

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This thesis presents five papers, studying enumerative and
extremal problems on combinatorial structures.
The first paper studies Forman's discrete Morse theory in the case where a group acts on…

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1 Introduccion These expository notes present several examples of how combinatorial methods can be used in Algebraic Geometry. The rst part describes the state and secondary polytopes and how they…

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The Hirsch Conjecture, posed in 1957, stated that the graph of a d-dimensional polytope or polyhedron with n facets cannot have diameter greater than n−d. The conjecture itself has been disproved,…

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Author(s): Wilson, Stedman | Advisor(s): Pak, Igor | Abstract: When does a topological polyhedral complex (embedded in Rd) admit a geometric realization (a rectilinear embedding in Rd)? What are the…

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- Computer Science, MathematicsJ. Comb. Theory, Ser. A
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This work provides two proofs of the following conjecture: a non-constructive proof introducing the notion of a pebble set of a polytope, and a constructive proof using a path-following argument.

Monograph

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Preface For every mathematician, ring theory and K-theory are intimately connected: algebraic K-theory is largely the K-theory of rings. At first sight, polytopes, by their very nature, must appear…

Hypergraph Polytopes

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We investigate a family of polytopes introduced by E.M. Feichtner, A. Postnikov and B. Sturmfels, which were named nestohedra. The vertices of these polytopes may intuitively be understood as…

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