3 problems

Let $r$-uniform set systems be families of $r$-element subsets of $[n]$. For nonnegative integers $a$ and a subset $X\subset[n]$, let $\mathcal{F}_{X,a}$ denote the corresponding e…

Sharp stability conjecture. There exists $B\in[n]^{(s)}$ such that

Tight uniform stability conjecture. There exists a $t$-umvirate $\mathcal{S}_B$ such that