(Re: Algorithm::Combinatorics) the logic in principle can be refined to skip some more permutations, but benchmarks showed no difference whatsoever, so I left the code that is easier to understand and added a comment about it:

/* I tried an alternative approach that would in theory avoid the
generation of some permutations with fixed-points: keeping track of
the leftmost fixed-point, and reversing the elements to its right.
But benchmarks up to n = 11 showed no difference whatsoever.
Thus, I left this version, which is simpler.
That n = 11 does not mean there was a difference for n = 12, it
means I stopped benchmarking at n = 11. */

The current interface guarantees lexicographic order, but I plan to provide more algorithms that relax that condition if you don't need it and faster generators are available. I will write it before I die ideally.