3 problems

Lecture hall position conjecture. If $\pi=\varphi(\lambda)$, then

Let $\ell_i$ denote the $i$-th Lecture Hall polynomial, constructed in the paper as a Laurent polynomial depending on $y_1,\dots,y_i$. Polynomiality conjecture for Lecture Hall pol…

Let $n\in\mathbb{N}$. There exist a $\mathbb{Z}^2$-graded polynomial ring $\Bbbk[x_1,\dots,x_m]$ for some $m\in\mathbb{N}$, a graded subalgebra $A_n\subseteq\Bbbk[x_1,\dots,x_m]$,…