Invertible transformations on permutation representations, including an RNG-free in-place Fisher-Yates-Knuth shuffle https://www.npmjs.com/package/factoradic

Permutations can be considered as the orbits of a dynamic system p' = succ(p), where p is a permutation and p' is its successor in the lexycographically ordered set of permutations (plus the Nil permutation, whose successor is Nil). Here I present a function that produces those orbits as well as a number of "permutation numbers" derived from tho…