Iterating shuffled [0..n) without arrays

Question

I know of a couple of routines that work as follows:

X_n+1 = Routine(X_n, max)

For example, something l

Answer 1

Is it possible to index a set of permutations without previously computing and storing the whole thing in memory? I tried something like this before and didn't find a solution - I think it is impossible (in the mathematical sense).

Disclaimer: I may have misunderstood your question...