A short proof of a conjecture of De Remer and Pennello

Bárány, Katchalski and Pach (Proc Am Math Soc 86(1):109---114, 1982) (see also Bárány et al., Am Math Mon 91(6):362---365, 1984) proved the following quantitative form of Helly's theorem. If the intersection of a family of convex sets in $$\mathbb {R}^d$...

In 1974 Chvátal conjectured that no intersecting family F in a downset can be larger than the largest star. In the same year Kleitman and Magnanti proved the conjecture when F is contained in the union of two stars, and Sterboul when ...

Ahlswede and Khachatrian [R. Ahlswede, L.H. Khachatrian, The complete nontrivial-intersection theorem for systems of finite sets, J. Combin. Theory Ser. A 76 (1996) 121-138] proved the following theorem, which answered a question of Frankl and Furedi [...