@article{Frankl2019SimpleJF,
title={Simple juntas for shifted families},
author={P. Frankl and A. Kupavskii},
journal={ArXiv},
year={2019},
volume={abs/1901.03816}
}

We say that a family $\mathcal F$ of $k$-element sets is a $j$-junta if there is a set $J$ of size $j$ such that, for any $F$, its presence in $\mathcal F$ depends on its intersection with $J$ only. Approximating arbitrary families by $j$-juntas with small $j$ is a recent powerful technique in extremal set theory. The weak point of all known approximation by juntas results is that they work in the range $n>Ck$, where $C$ is an extremely fast-growing function of the input parameters, such as the… CONTINUE READING