On Subdivisions of Simplicial Complexes: Characterizing Local h-Vectors.
We study the finite projective planes with linear programming models. We give a complete description of the convex hull of the finite projective planes of order 2. We give some integer linear programming models whose solution are, either a finite projective (or affine) plane of order n, or a (n+2)-arc.
The aim of the paper is to give an effective formula for the calculation of the probability that a random subset of an affine geometry AG(r-1,q) has rank r. Tables for the probabilities are given for small ranks. The expected time to the first moment at which a random subset of an affine geometry achieves the rank r is derived.