How Neighborly Can a Centrally Symmetric Polytope Be?

  • Authors:

  • Nathan Linial;Isabella Novik

  • Affiliations:

  • Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel;Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2006

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Abstract

We show that there exist k-neighborly centrally symmetric d-dimensional polytopes with 2(n + d) vertices, where $k(d,n)=\Theta\left(\frac{d}{1+\log ((d+n)/d)}\right).$ We also show that this bound is tight.