2 problems

Maximal-set realization conjecture. For every set of ideals $J_1,\ldots,J_s\in\textnormal{\textsf{S}}_{p(t)}^{n}$ such that

The Gröbner-fan maximality conjecture. For every cone of maximal dimension $\mathcal{C} \in \textnormal{GF}(\textnormal{\bf Hilb}_{p(t)}^{n})$, there exists a term order $\Omega$ s…