Given a permutation's lexicographic number, is it possible to get any item in it in O(1)

Question

I want to know whether the task explained below is even theoretically possible, and if so how I could do it.

You are given a space of N elements (i.e. all

Answer 1

All correct algorithms for accessing the kth item of a permutation stored in factoradic form must read the first k digits. This is because, regardless of the values of the other digits among the first k, it makes a difference whether an unread digit is a 0 or takes on its maximum value. That this is the case can be seen by tracing the canonical correct decoding program in two parallel executions.

For example, if we want to decode the third digit of the permutation 1?0, then for 100, that digit is 0, and for 110, that digit is 2.