Séminaire Lotharingien de Combinatoire, B11h (1984).
[Formerly: Publ. I.R.M.A. Strasbourg, 1985, 266/S-11, p.
On the Evolution of Finite Affine and Projective Spaces
Let q be a prime power, k<=m<=n integers.
Choose each of the
k-dimensional subspaces of
\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
determined: if \alpha(n)/f(n)
to 0 [resp. \infty,
then P(E) tends to 0 [resp.
1, nonzero constant]. The analogous
results for projective spaces are also obtained. The theorems
actually for some lattices. The above results,
as well as the lattice of subsets, are all special cases.
Geschäftsführer, Lufthansa Systems Berlin GmbH
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.