6 problems

For each $k$, let $m_{\ell}(k)$ denote the extremal quantity corresponding to the $\ell$-diversity introduced in the paper. Asymptotic vanishing-ratio conjecture. For all…

Linear-range low-degree conjecture. There is an absolute constant $c$ such that, whenever $n\geq ckt$,

Full-range low-degree vertex conjecture. If $n>2k$, then at least $n-2k$ vertices have degree at most

Let $\mathcal{F}\subset \binom{[n]}{k}$ be an intersecting family, and let $\gamma(\mathcal{F})$ denote its ordinary diversity. Suppose that $n>4k$. Ordinary diversity conjecture.…

For integers $r$ and $t$ with $2\leq t\leq r$, let an $(r,t)$-graph be an $r$-uniform, $r$-partite, $t$-intersecting hypergraph, and define … where $\tau(\mathcal H)$ is the cover…

Linear-edge construction conjecture. The function $f(r)$ grows linearly: