4 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…

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

Wilf–Zeilberger conjecture. A hypergeometric term is holonomic if and only if it is proper.

Monic recurrence conjecture. For every $\sigma\geq 1$, recurrences always exist in which the leading coefficients satisfy