Sperner theory
Algorithms counting monotone Boolean functions
Information Processing Letters
Minimal cut sets in biochemical reaction networks
Bioinformatics
Semi-Distance Codes and Steiner Systems
Graphs and Combinatorics
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Monotone Boolean functions (MBFs) are Boolean functions f:{0,1}^n-{0,1} satisfying the monotonicity condition x@?y@?f(x)@?f(y) for any x,y@?{0,1}^n. The number of MBFs in n variables is known as the nth Dedekind number. It is a longstanding computational challenge to determine these numbers exactly: these values are only known for n at most 8. Two monotone Boolean functions are equivalent if one can be obtained from the other by permuting the variables. The number of inequivalent MBFs in n variables was known only for up to n=6. In this paper we propose a strategy to count inequivalent MBFs 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.