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.

Largest family without A∪B⊆C∩D.

DE BONIS, Annalisa;
2005

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/1064069
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