Let be a set. A of is a bijection from to . We can think of a permutation of as a way of rearranging the elements in . The identity permutation is the permutation defined by .

• This is used to define the symmetric group and permutation groups.

definition.permutation.tex

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\begin{definition}
Let $X$ be a set.  A \textdef{permutation} of $X$ is a bijection from $X$ to $X$. We can think of a permutation of $X$ as a way of rearranging the elements in $X$. The identity permutation is the permutation $id_X:X\to X$ defined by $id_X(x)=x$.
\end{definition}

• Permutation