5 problems

The asymptotic invariant conjecture. The left-hand side of this inequality coincides with $\frac{1}{2}$ for every odd prime $p$:

Let $G$ be an enumerated graph. Let $\ell$ be the length of the longest induced path in $G$, and let $\ell_{<}$ be the length of the longest admissible path in $G$. Write…

Let $N$ be the net graph. Its binomial edge ideal is denoted by $J_N$, and write $\widehat{\operatorname{reg}}(J_N)$ for its asymptotic regularity. Net graph asymptotic regularity…

Let $k\geq 3$ and let $f$ be a $k$-tensor. Denote its asymptotic symmetric subrank by $\operatorname{\widetilde{Q}_{s}}(f)$ and its asymptotic subrank by $\widetilde{Q}(f)$. Asympt…

Non-alternating maximality conjecture. The alternating hypothesis in the corresponding proposition can be removed: every sequence of diagrammatically maximal links satisfies