Definition:Transposition

A transposition 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 $$\mathrm{Fix} \left({\rho}\right) = S - \left\{{r, s}\right\}$$.