Left Gog–GOGAm trapezoid equienumeration conjecture

For $k\leqslant n$, a left Gog or GOGAm trapezoid of shape $(n,k)$ is obtained from the corresponding triangle by retaining the $k$ leftmost diagonals. Left Gog–GOGAm trapezoid conjecture. For all $k\leqslant n$, the $(n,k)$ left Gog and GOGAm trapezoids are equienumerated. The paper gives a bijective proof for trapezoids with one or two diagonals, while the general case is posed as the conjectural extension.