The distinct displacement-pattern conjecture for permutations

Let $S_n$ be the symmetric group, and let a displacement pattern be a tuple $\alpha=(a_1,a_2,\dots,a_n)$ recording the displacements of a permutation, with the entries distinct. The necessary conditions are

$$\sum^m_{i=1}a_i\leq m(n-m)\quad(1\leq m\leq n),$$

with equality for $m=n$, together with the stated parity condition: if $n$ is even, the number of even entries is even, while if $n$ is odd, the number of odd entries is even. The distinct displacement-pattern conjecture. These necessary conditions are sufficient for the existence of a permutation $\pi\in S_n$ with displacement pattern $\alpha_\pi=\alpha$. The conjecture is identified as a special case of the perfect Skolem set conjecture. The source gives no separate resolution status.