4 problems

For each positive integer $n$, let $b_n(u)$ denote the factorially normalized Bernoulli polynomial of degree $n$, and consider the polynomial probability density $1-2^n b_n(u)$ on…

Exact minimum conjecture.

Let $d$ be fixed, let $\mathcal I_d$ be the set of weak $3$-compositions of $d$, and for every nonempty subset $\Gamma\subset\mathcal I_d$ let $M_\Gamma$ be the corresponding Berns…

The principal-minor positivity conjecture. For every such $\Gamma$, the matrix $M_\Gamma$ is nonsingular and