Eriksson–Linusson's realizability conjecture for permutation arrays

A permutation array is an element $P$ of $[n]^d$ satisfying the permutation-array conditions, and $X^o_P$ denotes the corresponding permutation array variety, consisting of tuples of flags in $\mathcal{F}l_n^d$ in relative position $P$. Eriksson–Linusson's realizability conjecture. Every permutation array can be realized by flags. Equivalently, every $X^o_P$ is nonempty. This conjecture asserts that the combinatorial permutation-array data always occur as the relative position of a tuple of flags; the supplied text gives no resolution status.