Inversion set and vector of a permutation

Example of inversions of a permutation

The example permutation (4,1,5,2,6,3) has the left inversion count (0,1,0,2,0,3)
and the inversion set { (1,2) , (1,4),(3,4) , (1,6),(3,6),(5,6) }.
The left inversion count converted to decimal is 373 - the permutation's reverse colexicographic rank.

(This permutation is also shown in this array.)

The inversion set contains 6 of the ${\displaystyle {\tbinom {6}{2}}}$ = 15 2-subsets of a 6-set.

 A018900