Abstract
A ranking function for the permutations on n symbols assigns a unique integer in the range [0,n!−1] to each of the n! permutations. The corresponding unranking function is the inverse: given an integer between 0 and n!−1, the value of the function is the permutation having this rank. We present simple ranking and unranking algorithms for permutations that can be computed using O(n) arithmetic operations.
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