Abstract:
The problem of enumeration of all Boolean functions of $n$ variables
of the rank $k$ from the Post classes $F^\mu_8$ is considered.
This problem expressed in terms of the set theory is equivalent
to the problem of enumeration of all
$k$-families
of different subsets of an
$n$-set
having the following property: any
$\mu$
members of such a family have a non-empty intersection. A formula for
calculating
the cardinalities of these classes in terms of the graph theory is obtained.
Explicit formulas for the cases
$\mu=2$,
$k\le 8$
(for
$k\le 6$ they are given at the end of this paper),
$\mu=3,4$,
$k\le 6$,
and for every
$n$
were generated by a computer. As a consequence respective results
for the classes
$F^\mu_5$ are obtained.