On Mubayi's Conjecture and conditionally intersecting sets

Adam Mammoliti, Thomas Britz

Mubayi's Conjecture states that if $\mathcal{F}$ is a family of $k$-sized subsets of $[n]=\{1,\dots ,n\}$ which, for $k\ge d\ge 2$, satisfies $A_1 \cap\cdots\cap A_d \neq \em…