Geodesic
On the Evolution of Finite Affine and Projective Spaces
Séminaire lotharingien de combinatoire, Tome 11 (1984)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Let q be a prime power, k=m=n integers. Choose each of the k-dimensional subspaces of (GF(q))n with probability \alpha(n). Denote by E the event that the above random set of k-dimensional subspaces contains all k-dimensional subspaces of some m-dimensional subspace. The threshold function f(n) of E is determined: if \alpha(n)/f(n) tends to 0 [resp. \infty, nonzero constant] then P(E) tends to 0 [resp. 1, nonzero constant]. The analogous results for projective spaces are also obtained. The theorems are formulated actually for some lattices. The above results, as well as the lattice of subsets, are all special cases. Geschäftsführer, Lufthansa Systems Berlin GmbH The following version is available:

The paper has been finally published under the same title in IX symposium on operations research. Part I. Sections 1-4 (Osnabrück, 1984), pp. 313-327, Methods Oper. Res., 49, Athenäum/Hain/Hanstein, Königstein, 1985. 

@article{SLC_1984_11_a7,
     author = {Bernd Voigt},
     title = {On the {Evolution} of {Finite} {Affine} and {Projective} {Spaces}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {11},
     year = {1984},
     url = {http://geodesic.mathdoc.fr/item/SLC_1984_11_a7/}
}
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Bernd Voigt. On the Evolution of Finite Affine and Projective Spaces. Séminaire lotharingien de combinatoire, Tome 11 (1984). http://geodesic.mathdoc.fr/item/SLC_1984_11_a7/