Revlex-initial 0/1-polytopes

We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial sets of 0/1-vectors. Thus for each n 2d , we consider the 0/1-knapsack polytope given by all 0/1-vectors x = (x1, . . . , xd) such that d-1 i=0 xi2i is at most n. The revlex-initial 0/1-polytopes have remarkable extremal properties. In particular, they have surprisingly low numbers of facets and small average degrees. Thus we establish the existence of 0/1-polytopes of given dimension d and prescribed number n of vertices, d < n 2d , with no more than 3d facets and with average degree bounded by d + 8. Despite these "lower bound" type extremal properties, we prove that the revlex-initial 0/1-polytopes satisfy the Mihail

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Rafael Gillmann, Volker Kaibel
• Keywords: Convex Hulls, D-1 I=0 Xi2i, Extremal Properties, JCT 2006