Hypercube Related Polytopes

Polytopes Related to the

In a previous paper we constructed a nite regular (abstract) 4-polytope of typ e f3; 3; pg, for each odd prime p. Here we extend this construction, allowing p to be any positive integer. Distinct polytopes of the same type can then arise, some of which may be chiral; but in each instance, facets and vertex gures are regular.

Polytopes Related to Some Polyhedral Norms. Polytopes Related to Some Polyhedral Norms

On Some Polytopes Contained in the 0, 1 Hypercube that Have a Small Chvátal Rank

In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of infeasible 0,1 vectors that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal...

Gorenstein Fano Polytopes Arising from Order Polytopes and Chain Polytopes

Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from a finite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ). In addition, the unimodular equivalence problem of O(P ) and C(P ) was studied by the first author and Nan Li. In the present paper, three integral convex polytopes Γ(O(P ),−O(Q)), Γ(O(P ),−C(Q...

Geometry of spaces between polytopes and related zonotopes . ∗

We study geometric parameters associated with the Banach spaces (IRn, ‖·‖k,q) normed by ‖x‖k,q = (∑ 1≤i≤k |〈x, ai〉| )1/q , where {ai}i≤N is a given sequence of N points in IRn, 1 ≤ k ≤ N , 1 ≤ q ≤ ∞ and {λi }i≥1 denotes the decreasing rearrangement of a sequence {λi}i≥1 ⊂ IR. ∗

Efficient Bregman Projections onto the Permutahedron and Related Polytopes

The problem of projecting onto the permutahedron PH(c)—the convex hull of all permutations of a fixed vector c—under a uniformly separable Bregman divergence is shown to be reducible to the Isotonic Optimization problem. This allows us to employ known fast algorithms to improve on several recent results on Bregman projections onto permutahedra. In addition, we present a new algorithm MergeAndPo...