I made a conjecture today
Start from $1, \ldots, n$, by interchanging the position of $i$ and $j$ where $i < j$ in each step, we are able to get any permutation of $\{1, \ldots, n\}$.
Do you think my conjecture is correct?
OK, it turns out this is very easy. What if we add the following extra constraint to the conjecture?
In each step we can only switch the position of $i$ and $j$ who are adjacent in current permutation.