# Definition:Transposition

## Definition

Let $S$ be a set.

A transposition on $S$ is a 2-cycle.

That is, a transposition is a permutation $\rho$ on a set $S$ which exchanges, or transposes, exactly two elements of $S$.

Thus if $\rho$ is a transposition which transposes two elements $r, s \in S$, it follows from the definition of fixed elements that:

$\Fix \rho = S \setminus \set {r, s}$

## Also known as

A transposition is colloquially known as a two-letter swap.