Largest family without A union B contained in C intersect D

Details Largest family without A union B contained in C intersect D Largest family without A union B contained in C intersect D

2004-07-22

arxiv.org/abs/math/0407373v1

J. Combin. Theory Ser. A 111 (2005), no. 2, 331--336

Mathematics

Combinatorics

6 pages

Scientific paper

10.1016/j.jcta.2005.01.002

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.

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