On the extreme points of a certain convex polytope

On extreme points of the PPT Polytope

The polytope of pointed pseudo triangulations was described in [RSS01]. This polytope is a combinatorial tool to observe all possible pseudo triangulations of a certain point set. Each point of the polytope refers to one possible pseudo triangulation of the point set. To polytope vertices are connected by an edge if their pseudo triangulations just differ in one edge-flip. Once we have a PPT-po...

On the convex hull of random points in a polytope

'This research was sponsored by the National Science Foundation under Grant No. ECS-8418392. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation or the US Government. On the Convex Hull of Random Points in a Polytope R e x A . D w y e r * ...

On Counting Integral Points in a Convex Rational Polytope

Given a convex rational polytope b = x ∈ n+ Ax= b , we consider the function b → f b , which counts the nonnegative integral points of b . A closed form expression of its -transform z → z is easily obtained so that f b can be computed as the inverse -transform of . We then provide two variants of an inversion algorithm. As a by-product, one of the algorithms provides the Ehrhart polynomial of a...

On the Volume of a Certain Polytope

Let n ≥ 2 be an integer and consider the set Tn of n× n permutation matrices π for which πij = 0 for j ≥ i+ 2. In this paper we study the convex hull of Tn, which we denote by Pn. Pn is a polytope of dimension ( n 2 ) . Our main purpose is to provide evidence for the following conjecture concerning its volume. Let vn denote the minimum volume of a simplex with vertices in the affine lattice spa...

Extreme Points of Polar Convex Sets