7 problems

Let $Q(x,y,t)$ be the generating series of a lattice walk in the quarter plane with small step set, and associate to the walk the group of birational automorphisms of…

Let $\mathcal Q$ be the class of 6909 non-trivial quarter-plane rules. Let $\mathcal E_{\mathrm{alg}}$, $\mathcal E_{\mathrm{Df}}$ and $\mathcal E_{\mathrm{nonDf}}$ be the sets of…

Let $\mathcal Q$ be the class of two-step rules, and let $\mathcal N_\ell$ denote the set of rules in $\mathcal Q$ whose symmetry group has order $\ell$, with $\ell=\infty$ allowed…

Let $\mathcal Q$ be the class of two-step rules, and let $G_e,G_n,G_w,G_s$ denote the corresponding groups for the four directions. Directional group-order conjecture. For every tw…

Let $P_m^{{\mathrel{\tikz{\draw (0ex,1ex) -- (0ex,0ex) -- (1ex,0ex) (-0.2ex,0ex)}}}}$ be the number of quarter-plane spiral walks of length $m$. Let…

A small-step model is a step set $\mathcal S\subset\{-1,0,1\}^2\setminus\{(0,0)\}$, considered up to isomorphism, with walks restricted to the quarter plane. Bousquet-Mélou and Mis…

Let $(X,Y)$ be a random walk in the quarter plane, and let its continuum limit be the corresponding limiting process. Suppose the asymptotic behavior of the random walk is describe…