Largest family without A union B contained in C intersect D

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

Largest family without A union B contained in C intersect D

Authors

De Bonis, Annalisa

Katona, Gyula O. H.

Swanepoel, Konrad J.

Description

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