are smaller than it, a number between 0 and , allowing for different values.

A pair of indices (i,j) with and is called an inversion of ?, and L(?)_i counts the number of inversions (i,j) with i fixed and varying j. It follows that is the total number of inversions of ?, which is also the number of adjacent transpositions that are needed to transform the permutation into the identity permutation. Other properties of the Lehmer code include that the lexicographical order of the