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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
Received: 12.11.1998

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


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