Intersections of iterated shadows

Hou Tin Chau; David Ellis; Marius Tiba

Intersections of iterated shadows

Combinatorics 2024-09-16 v2 Classical Analysis and ODEs

Authors: Hou Tin Chau , David Ellis , Marius Tiba

Abstract

We show that if $\mathcal{A} \subset {[n] \choose n/2}$ with measure bounded away from zero and from one, then the $\Omega(\sqrt{n})$ -iterated upper shadows of $\mathcal{A}$ and $\mathcal{A}^c$ intersect in a set of positive measure. This confirms (in a strong form) a conjecture of Friedgut. It can be seen as a stability result for the Kruskal--Katona theorem.

Keywords

intersection theory

Cite

@article{arxiv.2409.05487,
  title  = {Intersections of iterated shadows},
  author = {Hou Tin Chau and David Ellis and Marius Tiba},
  journal= {arXiv preprint arXiv:2409.05487},
  year   = {2024}
}

Comments

Minor corrections. 8 pages

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