4 problems

Let $B$ be a board, let $i$ and $k$ be positive integers, and let $P\in\mathbb{Z}[x]$ be a polynomial of degree $k-1$ satisfying … for every $x$ in an unbounded subset of…

Let $B$ be a board, let $S$ be an unbounded subset of $\mathbb{Z}$, and let $k$ be a positive integer. Say that $H_d(B,x+1)$ is polynomial modulo $x^k$ on $S$ if there is a polynom…

Deletion–contraction conjecture for $P(x;\lambda)$. One has

Nadeau–Tewari deletion–contraction conjecture. The $q$-hit numbers satisfy