Question: How to transform a permutation into numbers and vice versa (via Lehmer Code)

Dear all,

I hope everyone helps me about the problem of converting a permutation into numbers and vice versa on maple

Let S_n denote the set of all permutations of the set {0, 1, ..., n − 1}. 

Lehmer code is a bijective function l : S_n ->{0, 1, 2, ..., n! − 1}.

Define function l(S)=Sum(c_i x (n − 1 − i)! ) where S in S_n and c_i is the number of elements of the set { j > i | s_j < s_i }

Inverse Lehmer code is a bijective function l⁻¹ : {0, 1, 2, ..., n! − 1} -> S_n

For example: n=4 -->{0, 1, 2, 3}, for S = (0, 2, 1, 3) , so c₀ = 0, c₁ = 1 ( j=2 > i=1 and s_j = 1 < s_i = 2), c₂ = 0, c₃ = 0 -->

I(S) = 0 x (3-0)! + 1 x (3 - 1)! + 0 x (3-2)! + 0 x (3 - 3)! = 2! = 2. So I((0, 2, 1, 3)) =2  and I^-1(2) = (0, 2, 1, 3).

How to calculate I and I^-1 on maple? Please help me! Thanks alot.