4 problems

Algebraicity conjecture. For every such finite group model and Laurent polynomial $I$, the series $\widetilde C(x,y)$ is algebraic. When $I(x,y)=x^ay^b$, it is the generating funct…

Consider the seven Weyl models in Table … . Weyl-model algebraicity conjecture. For every one of these seven models, $A(x,y)$ is algebraic; consequently, $C(x,y)$ is D-finite. In a…

For $n\ge 2$, define the large-step model $\mathcal{H}_n$ by the Laurent polynomial … For $a,b\ge 1$, consider the orbit of $\mathcal{H}_n$ and whether the monomial fraction…

Let $C_{0,0}$ denote the generating function for Gessel-model walks in the three-quadrant region $\mathcal C$ starting from $(0,0)$. Gessel degree conjecture. The series $C_{0,0}$…