Maximum hitting for n sufficiently large

Abstract

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

arXiv commentVersion 2 corrects the calculation of the sizes of the set families appearing in the proof of the main theorem. It also incorporates a number of other smaller corrections and improvements suggested by the anonymous referees. 7 pages