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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
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\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
Linking options:
http://mi.mathnet.ru/eng/dm398https://doi.org/10.4213/dm398 http://mi.mathnet.ru/eng/dm/v11/i4/p127
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