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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.
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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