Random covers of finite homogeneous lattices - Alekseychuk, A.N. (Інститут математики НАН України, 2006)
We develop and extend some results for the scheme of independent random elements
distributed on a ﬁnite lattice. In particular, we introduce the concept of the cover of
a homogeneous lattice Ln of rank n and derive the exact equations and estimations
for the number of covers with a given number of blocks and for the total covers
number of the lattice Ln. A theorem about the asymptotic normality of the blocks
number in a random equiprobable cover of the lattice Ln is proved. The concept of
the cover index of the lattice Ln, that extend the notion of the cover index of a ﬁnite
set by its independent random subsets, is introduced. Applying the lattice moments
method, the limit distribution as n→∞ for the cover index of a subspace lattice of
the n-dimensional vector space over a ﬁnite ﬁeld is determined.