Example
We may write a permutation of S_n in various different ways:

• As a product of disjoint cycles;
• As a 2×n matrix;
• As a directed graph: there is an edge from i to j if the image of i is j;
• As a permutation matrix: in the i-th column there is a 1 in the j-th row if the image of i is the element j. All other entries in this column are 0.

In the example below you can see various different presentations of elements of S₈.