Category:Transpositions
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This category contains results about Transpositions.
Definitions specific to this category can be found in Definitions/Transpositions.
Let $S$ be a set.
A transposition on $S$ is a $2$-cycle.
That is, a transposition is a permutation $\rho$ on $S$ 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:
- $\Fix \rho = S \setminus \set {r, s}$
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