5 problems

Polynomial sunflower conjecture. There exist constants $c_1(p),c_2(p)>0$ such that whenever

A $w$-set system is a family of sets, each of cardinality $w$. For a set system $\mathcal F$, sample $S,S_1,S_2$ independently and uniformly from $\mathcal F$. Two-intersection sun…

Let $\beta(w)$ denote the largest $\kappa$ for which there exists an intersecting $\kappa$-regular $w$-set system. Here a $w$-set system is a family of sets of size at most $w$, an…

Let $w$ be a positive integer, let $\varepsilon>0$, and let a monotone width-$w$ DNF be a monotone DNF whose terms contain at most $w$ literals. An upper-bound DNF for $f$ satisfie…

A monotone DNF is a DNF containing no negated literals. In the improved upper-bound DNF compression conjecture, $f_{\mathrm{upper}}$ is an upper bound of $f$ when…