2 problems

Let $A$ be a finite alphabet of even order, let $n\geq3$, let $S_A$ be the symmetric group on $A$, and let $TG(i,\alpha,o)$ denote the $i$-ary Toffoli gate with permutation…

Let $A=\\{1,\dots,k\\}$ be a finite alphabet of even cardinality, and let $n\geq 2$. Write $B_n(A)$ for the group of invertible maps on $A^n$, let $(1,\dots,k)$ denote the correspo…