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English version: Journal of Applied and Industrial Mathematics, 2018, 12:4, 797–802 |
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Volume 25, No 4, 2018, P. 15-26 UDC 519.71
Keywords: $k$-intersecting family of subsets, monotone selfdual Boolean function, layer of Boolean cube. DOI: 10.17377/daio.2018.25.602 Yury A. Zuev 1 Received 11 December 2017 References[1] Yu. A. Zuev, Modern Discrete Mathematics: From Enumerative Combinatorics to Cryptography of the XXI Century, Librokom, Moscow, 2018 [Russian].[2] A. D. Korshunov, The number of $k$-nonseparated families of subsets of an $n$-element set ($k$-nonseparated Boolean functions). I. The case of even $n$ and $k = 2$, Diskretn. Anal. Issled. Oper., Ser. 1, 10, No. 4, 31–69, 2003 [Russian]. [3] A. D. Korshunov, The number of $k$-nonseparated families of subsets of an $n$-element set ($k$-nonseparated Boolean functions of $n$ variables). II. The case of odd $n$ and $k = 2$, Diskretn. Anal. Issled. Oper., Ser. 1, 12, No. 1, 12–70, 2005 [Russian]. [4] A. D. Korshunov, The number of $k$-nonseparated families of subsets of an $n$-element set ($k$-nonseparated Boolean functions of $n$-variables). III. The case of $k \ge 3$ and arbitrary $n$, Diskretn. Anal. Issled. Oper., Ser. 1, 12, No. 3, 60–70, 2005 [Russian]. [5] R. G. Nigmatullin, The Complexity of Boolean Functions, Nauka, Moscow, 1991 [Russian]. [6] A. A. Sapozhenko, On the number of antichains in multilevelled ranked posets, Diskretn. Mat., 1, No. 2, 110–128, 1989 [Russian]. Translated in Discrete Math. Appl., 1, No. 2, 149–169, 1991. [7] P. Erdös and D. J. Kleitman, Extremal problems among subsets of a set, Discrete Math., 8, 281–294, 1974. [8] P. Erdös, C. Ko, and R. Rado, Intersection theorems for systems of finite sets, Q. J. Math., Oxf. II. Ser., 12, 313–320, 1961. [9] D. J. Kleitman, On Dedekind’s problem: The number of monotone Boolean functions, Proc. Am. Math. Soc., 21, No. 3, 677–682, 1969. |
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