Stability through non-shadows
Abstract
We study families F⊂eq 2[n] with restricted intersections and prove a conjecture of Snevily in a stronger form for large n. We also obtain stability results for Kleitman's isodiametric inequality and families with bounded set-wise differences. Our proofs introduce a new twist to the classical linear algebra method, harnessing the non-shadows of F, which may be of independent interest.
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