Inversions. (Top) There are four inversions required to translate the sorted list [1 2 3 4] into the permutation [3 4 1 2]. The sum of the digits of the factoradic give the number of inversions required to translate one permutation into another. (Bottom) The grey squares indicate the set of permutations that have a single inversion distance from the original (black) permutations.
Magis and Price BMC Bioinformatics 2012 13:227 doi:10.1186/1471-2105-13-227