In One Line and Anywhere. Permutations as Linear Orders. Inversions

In Section 1.3, we looked at descents of permutations. That is, we studied instances in which an entry in a permutation was larger than the entry directly following it. A more comprehensive permutation statistic is that of inversions. This statistic will look for instances in which an entry of a permutation is smaller than some entry following it (not necessarily directly).