3 problems

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

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

Nadeau–Tewari sign conjecture. For fixed $j$, $a_j^{m,n}(\lambda,q)$ is a Laurent polynomial in $q$ whose coefficients are integers of the same sign.