Largest family without A union B contained in C intersect D

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

Cited by in corpus (10)

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• Intersecting $P$-free families
• On an extremal problem involving a pair of forbidden posets
• Avoiding Brooms, Forks, and Butterflies in the Linear Lattices
• Existence thresholds and Ramsey properties of random posets
• Families of Subsets Without a Given Poset in the Interval Chains
• Largest family without a pair of posets on consecutive levels of the Boolean lattice