Title:  Counting Inequivalent Monotone Boolean Functions

The nth Dedekind number is the numbers of Boolean functions on n variables that are monotone in the sense that when x<=y, then f(x)<=f(y); values are only known only up to n=8. We consider the problem of counting these functions up to equivalence via permutations of the variables, where values were known only up to n=6. We propose a strategy to count inequivalent MBF's by breaking the calculation into parts based on the profiles of these functions. As a result we are able to compute the number of inequivalent MBFs in 7 variables. The number obtained is 490013148.

This is joint work with Timothy Yusun.