3 problems

Huh–Matherne–Mészáros–St. Dizier conjecture. The support of a homogenized Grothendieck polynomial is precisely the set of integer points of some generalized permutahedron.

Mészáros–St. Dizier conjecture. The support of each Castelnuovo–Mumford polynomial is M-convex.

Let $k$ and $d$ be positive integers, and let $\lambda\in \mathrm{Par}^k(d)$ be a partition. The $k$-Schur polynomial associated with $\lambda$ is denoted by $s_{\lambda}^{(k)}$. M…