### Atom - `Œ?`

- Permutation for Index

Tags: `miscellaneous` , `array` , `combinatorics` , `vectorize`

##### Arity: monadic

This atom is monadic, which means it takes one argument.

##### Functionality

Find the shortest permutation of `[1, 2, ..., N]`

for some `N`

that yields `z`

when passed through `Œ¿`

(Permutation Index).

##### Details

Right inverse of `Œ¿`

. The permutation's length will be the minimum `N`

such that `z ≤ N!`

. Note that not every permutation is a possible output; for example, `[1, 3, 2]`

cannot be output because its permutation index is `2`

, which can be represented by `[2, 1]`

instead.