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Discussiones Mathematicae Graph Theory 20(2) (2000) 209-217
DOI: https://doi.org/10.7151/dmgt.1120

ON THE RANK OF RANDOM SUBSETS OF FINITE AFFINE GEOMETRY

Wojciech Kordecki

Institute of Mathematics
Wrocław University of Technology
Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
e-mail: kordecki@im.pwr.wroc.pl

Abstract

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.

Keywords: finite affine geometry, random matroids, hitting time.

2000 Mathematics Subject Classification: Primary: 05B25; Secondary: 51E20.

References

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[3]	W. Kordecki, Random matroids, Dissert. Math. CCCLXVII (PWN, Warszawa, 1997).
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Received 15 November 1999
Revised 24 November 2000