Derangement/Examples

Examples of Derangements

$3$ Element Set

Let $S = \set {1, 2, 3}$ be an arbitrary set with $3$ elements.

The only derangements of $S$ are the permutations $p_1$ and $p_2$ given in $2$-row notation as:

\(\ds p_1\)

\(:\)

\(\ds \begin {pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end {pmatrix}\)

\(\ds p_2\)

\(:\)

\(\ds \begin {pmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \end {pmatrix}\)