3 problems

Pemantle's conjecture. The ordinary convolution of a ULC($m$) sequence and a ULC($\ell$) sequence is ULC($m+\ell$), where $m$ and $\ell$ may be infinity. Ultra-log-concavity is clo…

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

Let a probability measure on the Boolean hypercube satisfy certain negative correlation conditions, and let $\{p_k\}$ be the sequence of probabilities of picking a set of size $k$.…