6 problems

Let $k$-noncrossing partitions be set partitions in which no $k$ arcs mutually cross, and let $k\geq 4$. A sequence is P-recursive if it satisfies a linear recurrence with polynomi…

Let ${\mathbf a}=(a_1,a_2,\dots,a_k)$ be a composition of $n$ into positive parts, and say that it contains $123$ if it has a subsequence order-isomorphic to $123$. Herb Wilf's con…

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

Let $H_n(3)$ denote the number of $n\times n$ $(0,1)$-matrices with every row and column sum equal to $3$. Yang's conjecture. The sequence $\{H_n(3)\}_{n\geq 2}$ is log-convex, nam…

Let $G$ be a nilpotent group, and consider the P-recursiveness property discussed in the preceding context: P-recursiveness of the relevant sequence for all symmetric generating se…

Undecidability conjecture. The problem of deciding whether $\bigl\{[1]u^n\bigr\}$ is P-recursive is undecidable.