Intersections of iterated shadows
Hou Tin Chau, David Ellis, Marius Tiba

TL;DR
This paper proves that for large subsets of the middle layer of the Boolean cube with measures bounded away from zero and one, their iterated shadows intersect significantly, confirming a conjecture of Friedgut and relating to the Kruskal--Katona theorem.
Contribution
It establishes a strong form of Friedgut's conjecture by showing intersection properties of iterated shadows for large subsets, providing a stability version of the Kruskal--Katona theorem.
Findings
Iterated shadows of large subsets intersect in positive measure.
Confirms Friedgut's conjecture in a strong form.
Provides a stability result for the Kruskal--Katona theorem.
Abstract
We show that if with measure bounded away from zero and from one, then the -iterated upper shadows of and 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsUrban Design and Spatial Analysis
