Definition:Transposition

Definition
A transposition (colloquially known as a two-letter swap) 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:
 * $\operatorname{Fix} \left({\rho}\right) = S - \left\{{r, s}\right\}$