2 problems

Let $F$ be a $k$-graph. For integers $1\leq\ell\leq k-3$, let $\pi_{\rm u}^{(\ell)}(F)$ denote its $\ell$-uniform Turán density. An $(\ell+1)$-vanishing order is an ordering of…

For integers $k\geq4$ and $\ell\geq3$ with $\ell<k$, let $F$ be a $k$-graph. An $\ell$-vanishing order of $F$ is an ordering of $V(F)$ admitting an $\ell$-vanishing coloring with t…