4 problems

Let $M_{\mathcal I_d}$ be the full degree-$d$ bivariate Bernstein collocation matrix, and denote its eigenvalues by $\lambda_{i,n}^{\langle d\rangle}$, where the second index recor…

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