Derangement/Examples
Jump to navigation
Jump to search
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:
\(\ds p_1\) | \(:\) | \(\ds \begin {pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end {pmatrix}\) | ||||||||||||
\(\ds p_2\) | \(:\) | \(\ds \begin {pmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \end {pmatrix}\) |