Largest family without A ∪ B ⊆ C ∩ D

Authors:
Annalisa De Bonis;Gyula O. H. Katona;Konrad J. Swanepoel
Affiliations:
University of Salerno, Salerno, Italy;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Science (HAS), Budapest, Hungary;Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, UNISA, South Africa
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

Citing 1
Cited 5

Sperner theory

Sperner theory

Note: No four subsets forming an N

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On diamond-free subposets of the Boolean lattice

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Sperner type theorems with excluded subposets

Discrete Applied Mathematics

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Abstract

Let F be a family of subsets of an n-element set not containing four distinct members such that A ∪ B ⊆ C ∩ 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.