Definition:Permutation on n Letters/Set of Permutations

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

The set of all permutations of $\N^*_n$ is denoted $S_n$.

Also denoted as
Some sources use $S \left({n}\right)$ for $S_n$.

Also see

 * Symmetric Group