Weak order of permutations

In computer science and discrete mathematics a sequence has an inversion where two of its elements are out of their natural order.

Let ${\displaystyle \pi }$ be a permutation. If ${\displaystyle i<j}$ and ${\displaystyle \pi (i)>\pi (j)}$, either the pair of places ${\displaystyle (i,j)}$ or the pair of elements ${\displaystyle {\bigl (}\pi (i),\pi (j){\bigr )}}$ is called an inversion of ${\displaystyle \pi }$.

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