Two-Row Notation/Examples
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Examples of Two-Row Notation
Permutations in $S_3$
The permutations on the symmetric group on $3$ letters $S_3$ can be depicted in two-row notation as:
- $\begin{pmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 2 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \end{pmatrix}$
- $\begin{pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \end{pmatrix} \qquad \begin{pmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{pmatrix}$
Permutation in $S_4$
The permutation on the symmetric group on $4$ letters $S_4$ defined as:
- $1 \mapsto 3, 2 \mapsto 2, 3 \mapsto 4, 4 \mapsto 1$
can be depicted in two-row notation as:
- $\begin{pmatrix} 1 & 2 & 3 & 4 \\ 3 & 2 & 4 & 1 \end{pmatrix}$