On the number of equivalence classes of invertible Boolean functions under action of permutation of variables on domain and range

TL;DR

This paper develops a method to compute the number of equivalence classes of invertible Boolean functions under variable permutations, extending known values from n ≤ 6 to n ≤ 30.

Contribution

The paper introduces a procedure to calculate the number of equivalence classes for invertible Boolean functions for larger n, up to 30, beyond previous known values.

Findings

Values of V_n computed for n ≤ 30

Extended the known range of equivalence class counts

Provided a systematic calculation procedure

Abstract

Let $V_n$ be the number of equivalence classes of invertible maps from $\{0,1\}^n$ to $\{0,1\}^n$, under action of permutation of variables on domain and range. So far, the values $V_n$ have been known for $n\le 6$. This paper describes the procedure by which the values of $V_n$ are calculated for $n\le 30$.