Do permutations such as those in the group $S_3$ move elements based on place (of elements in the input) or index?
move 1 to 2's place (e.g. if the input is 132, then the above permutation would result in 321) or to index 2 (in which case the input 132 would result in 312)?
where reading from right to left the left permutation is seen to move (on input 321) 1 to the place of 2, 2 to the place of 1 and 3 to the place of 3. So this works on places.