8 problems

Let ${\mathcal Y}$ be a step set for walks in the quarter plane, and let $Q_{\mathcal Y}$ denote its generating function. Assume that the step set group ${\mathcal Y}$ is not singu…

For a small-step quarter-plane model with stepset $S$, let $Q(x,y;t)$ be its generating function, and let $Q(0,1;t)$ and $Q(1,0;t)$ denote its two boundary specializations. The mod…

A small-step quarter-plane lattice model is determined by a stepset $S\subseteq\{-1,0,1\}^2\setminus\{(0,0)\}$, and its counting generating function is … where the sum ranges over…

Finite-group decoupling conjecture. A decoupling function can be computed if and only if the group of the walk is finite.

Conjectured 2sip inequality. For $0\leq t\leq t_c$, one has

Equal growth-rate conjecture. The radii of convergence of the two generating functions are equal. The conjecture is reduced to conjectures of Albert and Bousquet-Mélou concerning a…

Bousquet-Mélou–Mishna conjecture. Such a walk has a holonomic generating series if and only if its associated group is finite.

Let ${\mathfrak{S}}$ be a step set symmetric about an axis $L$, where $L$ passes through the first quadrant, potentially along a boundary. Let $L^\perp$ be the line perpendicular t…