Two-Row Notation/Examples

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}$