Definition:Permutation on n Letters

Definition
Let $\N_k$ be used to denote the initial segment of natural numbers:
 * $\N_k = \closedint 1 k = \set {1, 2, 3, \ldots, k}$

A permutation on $n$ letters is a permutation:
 * $\pi: \N_n \to \N_n$

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

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