Problem
1. Show that the permutation [n, n - 1, ... , 2, 1] has n (n - 1) inversions.
2. Give the transpose of the permutation [2, 5, 1, 6, 3, 4], and find the number of inversions in both permutations. What is the total number of inversions?
3. Show that there are n (n - 1) /2 inversions in a permutation of n distinct ordered elements with respect to its transpose.