# On the rank of random subsets of finite affine geometry

Discussiones Mathematicae Graph Theory (2000)

- Volume: 20, Issue: 2, page 209-217
- ISSN: 2083-5892

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topWojciech Kordecki. "On the rank of random subsets of finite affine geometry." Discussiones Mathematicae Graph Theory 20.2 (2000): 209-217. <http://eudml.org/doc/270147>.

@article{WojciechKordecki2000,

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.},

author = {Wojciech Kordecki},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {finite affine geometry; random matroids; hitting time; random subset; affine geometry},

language = {eng},

number = {2},

pages = {209-217},

title = {On the rank of random subsets of finite affine geometry},

url = {http://eudml.org/doc/270147},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Wojciech Kordecki

TI - On the rank of random subsets of finite affine geometry

JO - Discussiones Mathematicae Graph Theory

PY - 2000

VL - 20

IS - 2

SP - 209

EP - 217

AB - 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.

LA - eng

KW - finite affine geometry; random matroids; hitting time; random subset; affine geometry

UR - http://eudml.org/doc/270147

ER -

## References

top- [1] C.J. Colbourn and J.H. Dinitz, The CRC Handbook of Combinatorial Designs (CRC Press, Boca Raton, 1996). Zbl0836.00010
- [2] W. Kordecki, On the rank of a random submatroid of projective geometry, in: Random Graphs, Proc. of Random Graphs 2 (Poznań 1989, Wiley, 1992) 151-163. Zbl0816.60012
- [3] W. Kordecki, Random matroids, Dissert. Math. CCCLXVII (PWN, Warszawa, 1997). Zbl0934.05034
- [4] W. Kordecki, Reliability bounds for multistage structures with independent components, Statist. Probab. Lett. 34 (1997) 43-51, doi: 10.1016/S0167-7152(96)00164-2. Zbl0899.62129
- [5] M.V. Lomonosov, Bernoulli scheme with closure, Probl. Inf. Transmission 10 (1974) 73-81. Zbl0316.05020
- [6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).
- [7] B. Voigt, On the evolution of finite affine and projective spaces, Math. Oper. Res. 49 (1986) 313-327. Zbl0583.06006
- [8] D.J.A. Welsh, Matroid Theory (Academic Press, London, 1976).

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