A Centrally Symmetric Version of the Cyclic Polytope

✍ Scribed by Alexander Barvinok; Isabella Novik

• Publisher: Springer
• Year: 2007
• Tongue: English
• Weight: 506 KB
• Volume: 39
• Category: Article
• ISSN: 0179-5376
• DOI: 10.1007/s00454-007-9034-x

✦ Synopsis

We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces in all dimensions among all centrally symmetric polytopes with vertices of a given even dimension when is fixed and n grows. For a fixed even dimension and an integer we prove that the maximum possible number of -dimensional faces of a centrally symmetric -dimensional polytopewith vertices is at least for some and at most as grows.We show that and conjecture that the bound is best possible.