Category:Definitions/Derangements

This category contains definitions related to Derangements.
Related results can be found in Category:Derangements.

A derangement is a permutation $f: S \to S$ from a set $S$ to itself where:

$\forall s \in S: \map f s \ne s$

That is, a permutation with no fixed points.

If $S$ is finite, the number of derangements is denoted by $D_n$ or $d_n$, where $n = \card S$ (the cardinality of $S$.)