2 problems

Strong $q$-log-concavity conjecture. The polynomial sequence $\left(b_k(S;q)\right)_{k=\mathbf{h}(m)-m}^{\mathbf{h}(m)}$ is strongly $q$-log concave.

For a fixed positive integer $b$, let $\operatorname{inv}(a,b)$ denote the inversion number and let $I_n(b)$ be its $n$th smallest value, where $1\leq n\leq6$. Six-smallest-values…