Derangement/Examples/3 Element Set
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Example of Derangement
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:
\(\ds p_1\) | \(:\) | \(\ds \begin {pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end {pmatrix}\) | ||||||||||||
\(\ds p_2\) | \(:\) | \(\ds \begin {pmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \end {pmatrix}\) |
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): derangement