Maximum hitting for n sufficiently large

Abstract

For a left-compressed intersecting family contained in [n](r) and a set X contained in [n], let (X) = A in : A intersect X is non-empty. Borg asked: for which X is |(X)| maximised by taking to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.

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