A107765 Number of nonisomorphic self-dual monotone Boolean functions of n variables (where the result depends on all n variables).
1, 0, 1, 1, 4, 23, 686
Offset: 1
Examples
The four cases for n=5 can be represented as simple majority functions as follows: maj(a,b,c,d,e); maj(a,a,b,b,c,d,e); maj(a,a,a,b,b,c,c,d,e); maj(a,a,a,b,c,d,e). (Only 14 of the 23 cases for n=6 have a simple representation of this form.)
References
- S. Muroga. Threshold Logic and its Applications. Wiley, 1971.
- John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (1944), Section 52.5.
Crossrefs
Cf. A008840 (larger class of Boolean functions = partial sums of A107765). - Olivier Gérard, Oct 11 2012
Extensions
a(7) from Vladeta Jovovic, Jun 13 2005