Simple juntas for shifted families

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