On the number of Boolean functions in the Post classes $F_8^\mu$
Diskretnaya Matematika, Tome 11 (1999) no. 4, pp. 127-138
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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.
@article{DM_1999_11_4_a10,
author = {V. Jovovi\'c and G. Kilibarda},
title = {On the number of {Boolean} functions in the {Post} classes $F_8^\mu$},
journal = {Diskretnaya Matematika},
pages = {127--138},
publisher = {mathdoc},
volume = {11},
number = {4},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1999_11_4_a10/}
}
V. Jovović; G. Kilibarda. On the number of Boolean functions in the Post classes $F_8^\mu$. Diskretnaya Matematika, Tome 11 (1999) no. 4, pp. 127-138. http://geodesic.mathdoc.fr/item/DM_1999_11_4_a10/