I have a set $S$ of size $n=|S|$. I want the set of all $n!$ permutations of all $n$ elements of $S$, where permutations are represented as sequences, and not as bijections.
I have already seen this post, but it is not what I want. I don't want the permutation group or the symmetric group, I simply want the set of sequences.
For instance, $S=\{1,2,3\}$, and I want to obtain $\{(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)\}$.
Is there a notation to do that, and if not, is there a formula to obtain what I want?
Thank you for your help.