in reply to Faster alternative to Math::Combinatorics
I wrote my own Permutation module in this post .. but it looks like we may have different ideas about a permutation. Your example doesn't list all of the permutations of (0, 2, 3) in an array of four elements .. it just has arrays where the elements exist in ascending order. For example, (0, 0, 2, 0) isn't in your list, and I can't tell if that omission is intentional or not.
In any case, I'd write code to do the deed myself, and perhaps benchmark it against the module you've chosen -- it could be that your code is faster because it has less overhead. If that quick test fails, you may have to put on your thinking cap and simplify the algorithm. Or allocate a couple of hours to generate the test cases.