`forward_shuffle` is the (GROUP) INVERSE of `fisher_yates_shuffle`. `mirror_shuffle` is the (GROUP) CONJUGATE of `fisher_yates_shuffle` by the cyclic permutati

`forward_shuffle` is the (GROUP) INVERSE of `fisher_yates_shuffle`. `mirror_shuffle` is the (GROUP) CONJUGATE of `fisher_yates_shuffle` by the cyclic permutation (n-1,n-2,...,1,0). In group theory, CONJUGATEs are like changes of coordinates. In the present application, they reverse the index labels. The article said it, but it's worth distilling it. PS: Oh, here's another link. Denote by "S!", or less formally, the factorial of a set S, to mean the set of permutations of S. Fisher-Yates is equivalent to a bijection between (S+1)! and S! × (S+1).