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 Diskr. Mat., 1999, Volume 11, Issue 4, Pages 127–138 (Mi dm398)

On the number of Boolean functions in the Post classes $F_8^\mu$

V. Jovović, G. Kilibarda

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.

DOI: https://doi.org/10.4213/dm398

Full text: PDF file (1167 kB)

English version:
Discrete Mathematics and Applications, 1999, 9:6, 593–605

Bibliographic databases:

UDC: 519.7

Citation: V. Jovović, G. Kilibarda, “On the number of Boolean functions in the Post classes $F_8^\mu$”, Diskr. Mat., 11:4 (1999), 127–138; Discrete Math. Appl., 9:6 (1999), 593–605

Citation in format AMSBIB
\Bibitem{JovKil99} \by V.~Jovovi{\'c}, G.~Kilibarda \paper On the number of Boolean functions in the Post classes $F_8^\mu$ \jour Diskr. Mat. \yr 1999 \vol 11 \issue 4 \pages 127--138 \mathnet{http://mi.mathnet.ru/dm398} \crossref{https://doi.org/10.4213/dm398} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1761018} \zmath{https://zbmath.org/?q=an:0965.06017} \transl \jour Discrete Math. Appl. \yr 1999 \vol 9 \issue 6 \pages 593--605