Two Row Notation

Write the permutation like this:

$$\Big( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 4 & 2 & 1 & 3 \end{array}\Big)$$

where the example above indicates that the contents of box 1 moves to box 4, box 2 is unchanged, the ball in box 3 moves to box 1, and the ball in box 4 moves to box 3.

The advantage of this notation is that it is very easy to figure out where everything goes. The disadvantage is that it requires writing down each number twice. Since the top row can always be put in order, however, there is no real need to write it, so simply listing the second row is sufficient (assuming there is an obvious way to put the boxes in order). But there is a better way: