Largest family without A union B contained in C intersect D

Annalisa De Bonis; Gyula O. H. Katona; Konrad J. Swanepoel

doi:10.1016/j.jcta.2005.01.002

paper

Largest family without A union B contained in C intersect D

arXiv:math/0407373 · doi:10.1016/j.jcta.2005.01.002

Abstract

Let F be a family of subsets of an n-element set not containing four distinct members such that A union B is contained in C intersect D. It is proved that the maximum size of F under this condition is equal to the sum of the two largest binomial coefficients of order n. The maximum families are also characterized. A LYM-type inequality for such families is given, too.

6 pages