McNamara–Steingrímsson interval rank-unimodality conjecture

For permutations $\rho$ and $\tau$ with $\rho oeq \tau$ in the permutation pattern poset, let $[\rho,\tau]$ denote the interval of permutations $u$ satisfying $\rho oeq u oeq \tau$, ranked by permutation length. McNamara–Steingrímsson's conjecture. Every interval in the permutation pattern poset is rank-unimodal. The conjecture extends the principal-downset question and is presented as an open problem in the source.