Journal of Integer Sequences, Vol. 25 (2022), Article 22.7.7

On the Number of Inequivalent Monotone Boolean Functions of 8 Variables

Bartłomiej Pawelski
Institute of Informatics
University of Gdańsk
Wita Stwosza 57
80-952 Gdańsk


In this paper, we present algorithms for determining the number of fixed points in the set of monotone Boolean functions under a given permutation of input variables. Then, using Burnside's lemma, we determine the number of inequivalent monotone Boolean functions of 8 variables. The number obtained is 1,392,195,548,889,993,358.

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(Concerned with sequences A000041 A000372 A003182 A181897.)

Received March 29 2022; revised versions received April 6 2022; August 15 2022; August 19 2022; August 23 2022; August 31 2022. Published in Journal of Integer Sequences, September 21 2022.

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