On the number of inequivalent monotone Boolean functions of 9 variables

TL;DR

This paper reports the first calculation of the number of inequivalent monotone Boolean functions for 9 variables, revealing an extremely large count of over 789 quintillion, highlighting the complexity of these functions.

Contribution

It provides the first exact count of inequivalent monotone Boolean functions for 9 variables, a significant computational achievement.

Findings

Number of inequivalent monotone Boolean functions of 9 variables: 789,204,635,842,035,040,527,740,846,300,252,680

First known exact enumeration for 9-variable case

Demonstrates the computational feasibility of enumerating such functions at higher dimensions

Abstract

We provide the first-ever calculation of the number of inequivalent monotone Boolean functions of 9 variables, which is equal to 789,204,635,842,035,040,527,740,846,300,252,680.