# Inversion (in combinatorics)

From Encyclopedia of Mathematics

**Inversion** may refer to:

- An inversion of a permutation $\pi$ on the ordered set $\{1,2,\ldots,n\}$ is a pair $i < j$ such that $\pi(i) > \pi(j)$
- A transposition, a permutation that exchanges two elements
- A derangement, a permutation with no fixed points

**How to Cite This Entry:**

Inversion (in combinatorics).

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Inversion_(in_combinatorics)&oldid=39878