Kordecki, Wojciech On the rank of random subsets of finite affine geometry. (English) Zbl 0982.05029 Discuss. Math., Graph Theory 20, No. 2, 209-217 (2000). 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 Keywords:random matroids; hitting time; random subset; affine geometry PDF BibTeX XML Cite \textit{W. Kordecki}, Discuss. Math., Graph Theory 20, No. 2, 209--217 (2000; Zbl 0982.05029) Full Text: DOI Link