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

Notation

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

Reference