why wouldn't this simpler code work?

The attached code, based on the description:

There is also an inverse permutation P-1 for which P-1 P = P P-1 = I. It can be found by taking the functional inverse, or by reversing each ordered pair in the definition of a function as a set of ordered pairs (and then sorting the ordered pairs by their new first elements).

For example, the inverse of {2,3,1} is the inverse of {(1,2), (2,3), (3,1)}, which is {(2,1), (3,2), (1,3)}, or {(1,3), (2,1), (3,2)}, or {3,1,2}.

from:

http://www.efgh.com/math/algebra/permutations.htm

is much simpler (only 1 loop instead of 4 loops). Why not use this much simpler code?

I've looked into this page and a variety of sources on this and I have to admit I'm inclined to agreed with you. I think Lucian has made this harder that is actually needed to be.

Where your function would differ over the existing one is when does not contain a perfect sequence of integers. i.e. {4,1,2,7,3}. However, I can't see when it would be logical to do this.

I'll await feedback from Lucian, but upload you code as a draft for now.