9 problems

Let $f$ be an algebraic function analytic at $\infty$, and let $[n/n]$ denote its diagonal Padé approximants. A spurious pole is a pole of a Padé approximant in the sense defined i…

The algebraicity–diagonal–global-boundedness conjecture. The following statements are equivalent:

Let $(c_n)_{n\geq 0}$ be the sequence discussed in the paper, and for $(u,v)\in\mathbb{Q}^2$ define $\widetilde c_n=w^n(u)_n(v)_n c_n$, where $(u)_n$ and $(v)_n$ are Pochhammer sym…

Let $y(x)=\sum_{k\geq 0}a_kx^k\in\mathbb{Q}[[x]]$ be D-finite. Assume that the sequence $(a_k)_{k\geq 0}$ has at most geometric growth, that there exists $N\in\mathbb{N}$ such that…

Let $G(t;a,b)$ denote the generating function for the corresponding model, with parameters $t$, $a$, and $b$. Models 19 and 20 are the Kreweras and reverse Kreweras walks, respecti…

The parametric algebraic-form conjecture.

Let $m\geq4$ and let $\tau=134\ldots(m-1)2m$ be the consecutive pattern of length $m$. Let $T(x)$ be the cluster generating function specified by the preceding conjectural hypergeo…

Balanced algebraic-function conjecture. Every such $P(\mathcal C,z)$ admits a positive motherbody measure.

Non-algebraicity conjecture. The generating function $D(z)$ is not algebraic.