3 problems

Ultra-log-concavity conjecture. For every $\pi\in\mathfrak{S}_n$, $Q_W^\pi$ is ultra-log-concave.

Ultra log-concavity conjecture. For every graph $G$, $D(G,x)$ is ultra log-concave.

Let $d_\ell(m)$ be the coefficient of $x^\ell$ in the Boros-Moll polynomial $P_m(x)$. For each fixed $\ell\geq 0$, define the sequence $a_m=d_\ell(m-1)d_\ell(m+1)/d_\ell^2(m)$ for…