Finite permutation - Knowlpedia

For $n\in\mathbb N$ , write $[n]=\{1,\ldots,n\}$ (with $[0]=\varnothing$ ). A finite permutation of size $n$ is a bijective function $\sigma:[n]\to[n]$ . The set of all such permutations is denoted $S_n$ .

Notation

In one-line notation, $\sigma$ is recorded as $(\sigma(1),\ldots,\sigma(n))$ , which contains each element of $[n]$ exactly once.

Reference

Konarovskyi, Mathematics 2, §6.1.