The Graßmann-Tamari lattice conjecture

Let $\mathcal{T}_{k,n}$ denote the Graßmann-Tamari poset on the relevant Graßmannian tableaux. The usual Tamari order is recovered when $k=2$. Graßmann-Tamari lattice conjecture. For general $k$, the Graßmann-Tamari poset $\mathcal{T}_{k,n}$ is a lattice. The conjecture is motivated by the self-dual lattice structure of the ordinary Tamari order and was tested in the source for $k=3$ and $n\in\{6,7,8\}$; no resolution is supplied.