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A245079 Number of bipolar Boolean functions, that is, Boolean functions that are monotone or antimonotone in each argument. 0
2, 4, 14, 104, 2170, 230540, 499596550, 30907579915064, 5483950159845307762 (list; graph; refs; listen; history; text; internal format)



A Boolean function is bipolar if and only if for each argument index i, the function is one of: (1) monotone in argument i, (2) antimonotone in argument i, (3) both monotone and antimonotone in argument i.


Richard Dedekind,Uber Zerlegungen von Zahlen durch ihre grossten gemeinsamen Theiler, in Fest-Schrift der Herzoglichen Technischen Hochschule Carolo-Wilhelmina, pages 1-40. Vieweg+Teubner Verlag (1897).


Table of n, a(n) for n=0..8.

Ringo Baumann and Hannes Strass, On the Number of Bipolar Boolean Functions, Journal of Logic and Computation, exx025. Also available as a Preprint.

G. Brewka and S. Woltran, Abstract dialectical frameworks, Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning. Pages 102--111. IJCAI/AAAI 2010.


a(n) = Sum_{i=1..n}(2^i * C(n,i) * A006126(i)) + 2.


There are 2 bipolar Boolean functions in 0 arguments, the constants true and false.

All 4 Boolean functions in one argument are bipolar.

For 2 arguments, only equivalence and exclusive-or are not bipolar, 16-2=14.


Cf. A006126.

Sequence in context: A005737 A219767 A000609 * A167008 A238638 A240973

Adjacent sequences:  A245076 A245077 A245078 * A245080 A245081 A245082




Hannes Strass, Jul 11 2014



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Last modified December 16 17:02 EST 2018. Contains 318172 sequences. (Running on oeis4.)