Simple 0/1-Polytopes

✍ Scribed by Volker Kaibel; Martin Wolff

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 100 KB
• Volume: 21
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1999.0328

✦ Synopsis

For general polytopes, it has turned out that with respect to many questions it suffices to consider only the simple polytopes, i.e., d-dimensional polytopes where every vertex is contained in only d facets. In this paper, we show that the situation is very different within the class of 0/1-polytopes, since every simple 0/1-polytope is the (cartesian) product of some 0/1-simplices (which proves a conjecture of Ziegler), and thus, the restriction to simple 0/1-polytopes leaves only a very small class of objects with a rather trivial structure.