8 problems

Symmetric polynomial enumeration conjecture.

Polynomial enumeration conjecture. For $n\geq 3$,

Enumeration conjecture. The number of corners in the set of symmetric tree-like tableaux of size $2n+1$ is

Enumeration conjecture. The number of corners in the set of tree-like tableaux of size $n$ is

The $(a,b)$-analogue conjecture. For $n\geq 3$,

L.-Z.'s corner enumeration conjecture. The number of corners in the set of tree-like tableaux of size $n$ is

Let $\mathcal T^{\mathrm{Sym}}_{2n+1}$ denote the set of symmetric tree-like tableaux of size $2n+1$, and let a corner be a corner of such a tableau. Symmetric corner enumeration c…

Let $\mathcal T_n$ denote the set of tree-like tableaux of size $n$, and let a corner be a corner of such a tableau. Corner enumeration conjecture. The total number of corners amon…