Consider the following list of permutations of {0,1,2,3,4,5,6,*,*,*} as generated with ordinary backtracking:
Index Permutation
1. 0123456***
2. 012345*6**
3. 012345**6*
4. 012345***6
5. 0123465***
...
60480. ***6543210
Is it there an O(1) function which, for any permutation gives back the permutation's index?