# permutation

## permutation

Bijection of a set in itself.

A permutation of the n objects of a set E is all ordered combinations of these n elements. Therefore, a permutation of n objects in a set E of n elements is an n-tuple formed by these elements.
If E $$= \left\{0, 1, 2, 3\right\}$$, then a permutation of E could be represented by the quadruplet $$\left(1, 0, 3, 2\right)$$, or the matrix: $$\begin{pmatrix} 0 & 1 & 2 & 3\\1 & 0 & 3 & 2\end{pmatrix}$$.

We can also describe a permutation as the set of ordered pairs that form the relation. In the previous case, we would have: {(0, 1), (1, 0), (2, 3), (3, 2)}.

A permutation of a set of n elements is an arrangement of these n objects taken n at a time.

### Form

The number of permutations in a set E that includes n elements is equal to n!.

### Example

Consider the set E = {0, 1, 2).
Therefore, we have: n! = 3! = 6.
The set of permutations of E is {(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)}.