3 problems

For each $n,k$, consider left Gog and GOGAm trapezoids of shape $(n,k)$, and let $X_{1,1}=l$ denote their bottom entry. Refined left Gog–GOGAm conjecture. For each $n,k,l$, the…

For Gog, Magog and GOGAm triangles, define the statistics $\alpha$, $\beta$, and $\gamma$ as in the paper; in particular, $\alpha_{\mathrm{Gog}}(X)$ counts indices $k$ with…

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 con…