On the Number of Inequivalent Monotone Boolean Functions of 9 Variables

The problem of counting all inequivalent monotone Boolean functions of nine variables is considered. We solve the problem using known algorithms and deriving new ones when necessary. We describe methods to count fixed points in sets of all monotone Boolean functions under a given permutation of input variables. With these techniques as a basis, we tabulate the cardinalities of these sets for nine variables. By applying Burnside's lemma and the numbers obtained, we calculate the number of inequivalent monotone Boolean functions of 9 variables, which equals 789,204,635,842,035,040,527,740,846,300,252,680.