Inversion

In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order.

Let $\pi$ be a permutation. There is an inversion of $\pi$ between $i$ and $j$ if $i<j$ and $\pi (i)>\pi (j)$. The inversion is indicated by an ordered pair containing either the places $(i,j)$ or the elements $(\pi (i),\pi (j))$