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On the rank of random subsets of finite affine geometry. (English) Zbl 0982.05029
Summary: 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 \(\text{AG}(r- 1,q)\) 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.
MSC:
05B25 Combinatorial aspects of finite geometries
51E20 Combinatorial structures in finite projective spaces
05B35 Combinatorial aspects of matroids and geometric lattices
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