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Lectures on 0/1-Polytopes

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Polytopes — Combinatorics and Computation

Part of the book series: DMV Seminar ((OWS,volume 29))

Abstract

These lectures on the combinatorics and geometry of 0/1-polytopes are meant as anintroductionandinvitation.Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects; all of them are related to some quite recent work and progress.

0/1-polytopes have a very simple definition and explicit de& riptions; we can enumerate and analyze small examples explicitly in the computer (e. g. using polymake). However, any intuition that is derived from the analysis of examples in “low dimensions” will miss the true complexity of 0/1-polytopes. Thus, in the following we will study several aspects of the complexity of higher-dimensional 0/1-polytopes: the doubly-exponential number of combinatorial types, the number of facets which can be huge, and the coefficients of defining inequalities which sometimes turn out to be extremely large. Some of the effects and results will be backed by proofs in the course of these lectures; we will also be able to verify some of them on explicit examples, which are accessible as a polymake database.

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Authors and Affiliations

  1. Dept. Mathematics, MA 7-1, Technische Universität Berlin, Berlin, 10623, Germany

    Günter M. Ziegler

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  1. Günter M. Ziegler
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Editors and Affiliations

  1. Institute of Mathematics and Computer Science, The Hebrew University, Givat Ram, 91904, Jerusalem, Israel

    Gil Kalai

  2. Fachbereich Mathematik MA 7-1, Technische Universität Berlin, Strasse des 17. Juni 135, D-10623, Berlin, Germany

    Günter M. Ziegler

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Ziegler, G.M. (2000). Lectures on 0/1-Polytopes. In: Kalai, G., Ziegler, G.M. (eds) Polytopes — Combinatorics and Computation. DMV Seminar, vol 29. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8438-9_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8438-9_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-6351-2

  • Online ISBN: 978-3-0348-8438-9

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