On the Number of Equivalence Classes of Invertible Boolean Functions under Action of Permutation of Variables on Domain and Range

Marko Carić, Miodrag Živković

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 $n\leq 6$. This paper describes the procedure by which the values of $V_n$ are calculated for $n\leq 30$.