Beating the Ahlswede--Khachatrian bound for the Erdős--Frankl--Pach problem

Tuan Tran, Zixiang Xu

In the 1980s, Erdős and, independently, Frankl and Pach conjectured that, for sufficiently large $n$, every $(d+1)$-uniform family on $\{1,\dots ,n\}$ with VC-dimension $d$ has si…