Definition:Permutation on n Letters

Definition
Let $\N^*_{\le k}$ be defined as the initial segment of natural numbers:
 * $\N^*_{\le k} = \left[{1 \,.\,.\, k}\right] = \left\{{1, 2, 3, \ldots, k}\right\}$

A permutation on $n$ letters is a permutation:
 * $\pi: \N^*_{\le n} \to \N^*_{\le n}$

The usual symbols for denoting a general permutation are $\pi$ (not to be confused with the famous circumference over diameter), $\rho$ and $\sigma$.

Set of All Permutations
The set of all permutations of $n$ letters is denoted $S_n$.

Cycle Notation
The two-row notation is a cumbersome way of defining a permutation.

Instead, the cycle notation is usually used instead.

Also see

 * Definition:Symmetric Group