Shuffling
\((a,b,c)\)
\((a,c,b)\)
\((b,a,c)\)
\((b,c,a)\)
\((c,a,b)\)
\((c,b,a)\)
Actions
\((0, 1, 2) \rightarrow (0,1,2)\)
\((0, 1, 2) \rightarrow (0,2,1)\)
\((0, 1, 2) \rightarrow (1,0,2)\)
\((0, 1, 2) \rightarrow (1,2,0)\)
\((0, 1, 2) \rightarrow (2,0,1)\)
\((0, 1, 2) \rightarrow (2,1,0)\)
Positional Notation
Apply \((1,0,2)\) to \((a,b,c)\) giving \((b,a,c)\).
Sometimes written as
\(\begin{pmatrix} 0 & 1 & 2 \\ 1 & 0 & 2 \end{pmatrix}\)
Combining Permutations
Apply \((1, 0, 2)(2, 1, 0)\) to \((a,b,c)\).
First, apply \((2,1,0)\) to \((a,b,c)\) giving \((c,b,a)\).
Then apply \((1,0,2)\) to \((c,b,a)\) giving \((b,c,a)\)
Note that we can apply \((1,0,2)\) to \((2,1,0)\) giving \((1,2,0)\).
See \((1,2,0)\) applied to \((a,b,c)\) also gives \((b,c,a)\).