Suppose I have a finite set $X$. Is there a standard notation to denote the set of all possible permutations of the elements of $X$?
P.S. something like the power set notation for all subsets.
Notation – All Permutations of a Set
notation
notation
Suppose I have a finite set $X$. Is there a standard notation to denote the set of all possible permutations of the elements of $X$?
P.S. something like the power set notation for all subsets.
Best Answer
The group of the permutations of $X$ (even if $X$ is infinite) is denoted by : $S(X)$, $\mathrm{Aut}(X)$, or $\mathfrak{S}(X)$.
If $X$ is finite with $n$ elements, it is denoted by $S_n$ or $\mathfrak S_n$.