On the number of inequivalent monotone Boolean functions of 8 variables

TL;DR

This paper develops algorithms and applies Burnside's lemma to accurately count the number of inequivalent monotone Boolean functions of 8 variables, revealing a precise and large enumeration.

Contribution

The paper introduces algorithms for fixed point determination and applies group action counting to find the exact number of inequivalent functions for 8 variables.

Findings

Number of inequivalent monotone Boolean functions of 8 variables: 1,392,195,548,889,993,358

Algorithms for fixed point analysis of Boolean functions

Application of Burnside's lemma to combinatorial enumeration

Abstract

In this paper, the author presents algorithms that allow determining the number of fixed points in permutations of a set of monotone Boolean functions. Then, using Burnside's lemma, the author determines the number of inequivalent monotone Boolean functions of 8 variables. The number obtained is 1,392,195,548,889,993,358.