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;
2005-01-01
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.File in questo prodotto:
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