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On the convex hull of projective planes

Jean-François Maurras, Roumen Nedev (2008)

RAIRO - Operations Research

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.

On the rank of random subsets of finite affine geometry

Wojciech Kordecki (2000)

Discussiones Mathematicae Graph Theory

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.

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