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Diskretnaya Matematika, 1999, Volume 11, Issue 4, Pages 127–138
DOI: https://doi.org/10.4213/dm398
(Mi dm398)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the number of Boolean functions in the Post classes Fμ8

V. Jovović, G. Kilibarda
Abstract: The problem of enumeration of all Boolean functions of n variables of the rank k from the Post classes Fμ8 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 μ 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 μ=2, k8 (for k6 they are given at the end of this paper), μ=3,4, k6, and for every n were generated by a computer. As a consequence respective results for the classes Fμ5 are obtained.
Received: 12.11.1998
Bibliographic databases:
UDC: 519.7
Language: Russian
Citation: V. Jovović, G. Kilibarda, “On the number of Boolean functions in the Post classes Fμ8”, 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://mathscinet.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:
  • https://www.mathnet.ru/eng/dm398
  • https://doi.org/10.4213/dm398
  • https://www.mathnet.ru/eng/dm/v11/i4/p127
  • This publication is cited in the following 2 articles:
    1. Kozyra P.M., “On the Number of Antichains and Antichain Covers of Labeled Sets”, J. Integer Seq., 24:4 (2021), 21.4.7  isi
    2. Ilya Shmulevich, Harri Lähdesmäki, Edward R. Dougherty, Jaakko Astola, Wei Zhang, “The role of certain Post classes in Boolean network models of genetic networks”, Proc. Natl. Acad. Sci. U.S.A., 100:19 (2003), 10734  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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