How many facets can a 0-1 polytope with vertices in have?

Let denote the maximum number of facets of a 0-1 polytope in . The question such as ``is this function bounded by an exponential in ?'' was open just until recently. The negative answer was given by Bárány and Pór who proved the superexponential behavior of .

This is a recent breakthrough in the theory of 0-1 polytopes.

Komei Fukuda 2004-08-26