Upper bounds on the maximal number of facets of 0/1-polytopes (Q1964653)

A polytope is said to be 0/1-polytope if it has only vertices with 0/1-coordinates. The authors prove the following two upper bounds on the number of facets \(f(d)\) that a \(d\)-dimensional 0/1-polytope can have: \(f(d)\leq 2(d-1)!+2(d-1)\) and \(f(d)=O((d-2)!)\). The first bound is the best one currently known for small dimensions, while the second bound is the best known for large dimensions.