### Atom - `œ¿`

- Permutation Index By Key

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

##### Arity: dyadic

This atom is dyadic, which means it takes two arguments.

##### Functionality

Find the permutation index of `x`

where the base permutation is `x`

sorted by index in `y`

.

##### Details

For example, to compute `1,2,3 œ¿ 3,4,1,2`

, we first sort `x`

by its indices in `y`

, which gives us `[3, 1, 2]`

. Then, we find the permutation index of `[1, 2, 3]`

in all permutations of `[3, 1, 2]`

. The latter's permutations are `[[3, 1, 2], [3, 2, 1], [1, 3, 2], [1, 2, 3], [2, 3, 1], [2, 1, 3]]`

, so the result is `4`

.