4 problems

Oeding's conjecture. All secant varieties of Segre products of projective spaces are arithmetically Cohen–Macaulay; equivalently, $\widehat{\sigma}_r$ is Cohen–Macaulay for every…

Let $A\in\operatorname{ASM}(n)$ be an alternating sign matrix, and let $1\oplus A\in\operatorname{ASM}(n+1)$ be the direct sum of the $1\times1$ identity matrix with $A$. Cohen–Mac…

Cohen–Macaulayness conjecture. The poset $\operatorname{\mathcal{S}}((V,\Psi),\mathbin{\perp})$ is Cohen–Macaulay.

Let $G$ be a finite simple graph on vertex set $[n]$. For $S\subseteq[n]$, let $c_G(S)$ be the number of connected components of $G-S$, and call $S$ a cut set if…