J. Gorodkin
Discrete Applied Mathematics 75, 269-275, 1997.
Abstract
The group of congruences and permutations of the two-colored
N-dimensional Boolean cube is considered. The total number of orbits
generated by these automorphisms are shown to scale as
22N/(2N+1N!) when
N tends to infinity. The probability that a randomly chosen function
will belong to an orbit containing the maximum possible number of elements,
2N+1N!, approaches one as N goes to infinity.
Simulations for N<=6 are in agreement with the scaling predictions.
Keyword(s): Boolean functions; Orbits; Equivalence classes; Counting;
Neural networks