4 problems

Let $k\geq1$, $1\leq\ell\leq k$, $1\leq i\leq k+1$, $1\leq i'\leq\ell+1$, and $|q|<1$. Let $C_k$ be the Cartan matrix of type $A_k$, let $B_{\ell-1}$ be the inverse Cartan matrix o…

Let $k\geq 1$, $1\leq \ell\leq k$, $1\leq i\leq k+1$, $1\leq i'\leq \ell+1$, and let $L$ satisfy $\ell L\geq k+\ell-i-i'+2$. Let $C_k$ and ${\cal I}_k$ denote the Cartan and incide…

Finite Andrews–Gordon Bailey hierarchy conjecture.

Finite companion Andrews–Gordon conjecture.