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