Intersections of iterated shadows

2024/09/09 by Chau, Hou Tin, Ellis, David, Tiba, Marius
#05D05 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.05487

Abstract

We show that if A ⊂ [n] \choose n/2 with measure bounded away from zero and from one, then the Ω(√(n))-iterated upper shadows of A and 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.

Related

• Tight bounds for Katona's shadow intersection theorem
• Stability through non-shadows
• Asymptotic upper bounds on the shades of t-intersecting families
• On strengthenings of the intersecting shadow theorem
• A local version of Katona's intersection theorem