Inversion (discrete mathematics)

Pair of positions in a sequence where two elements are out of sorted order

Permutation with one of its inversions highlighted. An inversion may be denoted by the pair of places (2, 4) or the pair of elements (5, 2). The inversions of this permutation using element-based notation are: (3, 1), (3, 2), (5, 1), (5, 2), and (5,4).

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