Is there a formula to find a permutation from a given rank?

Question

Observing, for example, a set of permutations from 4 choose 2:

1. [1, 2]
2. [1, 3]
3. [1, 4]
4. [2, 3]
5. [2, 4]
6. [3, 4]

Does such a formula exist to go from a permutation's rank to the values of it's permutation (ex. 2 -> [1,3]) without first generating the possibilities algorithmically?