2000 character limit reached
Intersections of iterated shadows (2409.05487v2)
Published 9 Sep 2024 in math.CO and math.CA
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.