Permutation/Inversion/Definition

Let ${\displaystyle {}M=\{1,\ldots ,n\}}$, and let ${\displaystyle {}\pi }$ be a permutation on ${\displaystyle {}M}$. We call an index pair

${\displaystyle {}i<j\,}$

an inversion (of ${\displaystyle {}\pi }$), if ${\displaystyle {}\pi (i)>\pi (j)}$ holds.