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Number of Boolean functions of n variables that are self-dual and regular.
5

%I #44 Sep 03 2024 08:26:14

%S 0,1,1,2,3,7,21,135,2470,319124,1214554343,1706241214185942

%N Number of Boolean functions of n variables that are self-dual and regular.

%C Or, number of self-dual 2-monotonic Boolean functions of n or fewer variables.

%C Agrees with A001532 for n <= 8 but then diverges.

%C The value for n=10 was calculated with BDD techniques; all solutions are characterized by a binary decision diagram with 30011986 nodes.

%C The value for n=11 was calculated by Minfeng Wang in May 2012 (see [Hausmann & Rodriguez]). The news was published by J.-C. Hausmann (2015). - _Fabián Riquelme_, Mar 19 2018

%C For n from 1 to 9, a(n) agrees with the number of directed zero-sum games with n players in Table 1 of Krohn and Sudhölter. - _Peter Bala_, Dec 16 2021

%D D. E. Knuth, The Art of Computer Programming, Vol. 4, Section 7.1.1 (in preparation).

%H Jean-Claude Hausmann, <a href="http://arxiv.org/abs/1501.07553">Counting polygon spaces, Boolean functions and majority games</a>, arXiv preprint arXiv:1501.07553 [math.CO], 2015.

%H Jean-Claude Hausmann and Eugenio Rodriguez, <a href="http://www.unige.ch/math/folks/hausmann/polygones/">The space of clouds in an Euclidean space</a>, Corrections and additional material, 2014.

%H I. Krohn and P. Sudhölter, <a href="https://doi.org/10.1007/BF01415753">Directed and weighted majority games</a>, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, row 4, p. 213; also on <a href="https://www.researchgate.net/publication/226788682_Directed_and_weighted_majority_games">ResearchGate</a>.

%H S. Muroga, T. Tsuboi and C. R. Baugh, <a href="https://people.eecs.berkeley.edu/~alanmi/publications/other/01671639_002.pdf">Enumeration of threshold functions of eight variables</a>, IEEE Trans. Computers, 19 (1970), 818-825.

%K nonn,hard,more

%O 0,4

%A _Don Knuth_, Aug 17 2005

%E a(10) from _Don Knuth_, Feb 06 2008

%E a(11) from _Fabián Riquelme_, Mar 27 2018