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On 0-1 Polytopes with Many Facets

✍ Scribed by Imre Bárány; Attila Pór

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
159 KB
Volume
161
Category
Article
ISSN
0001-8708

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✦ Synopsis

There exist n-dimensional 0-1 polytopes with as many as ( cn log n ) nÂ4 facets. This is our main result. It answers a question of Komei Fukuda and Gu nter M. Ziegler.

📜 SIMILAR VOLUMES

Upper Bounds on the Maximal Number of Fa
Upper Bounds on the Maximal Number of Facets of 0/1-Polytopes
✍ Tamás Fleiner; Volker Kaibel; Günter Rote 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 157 KB

We prove two new upper bounds on the number of facets that a d-dimensional 0/1-polytope can have. The first one is 2(d -1)!+2(d -1) (which is the best one currently known for small dimensions), while the second one of O((d -2)!) is the best known bound for large dimensions.