Bounds on Maximal Families of Sets Not Containing Three Sets with A ∩ B ⊂ C, A ⊄ B
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Lower and upper estimates are given on the size of a family of subsets of an n-element set containing no three distinct sets satisfying A ∩ B ⊂ C, A ⊄ B. This is a sharpening of an earlier result where the same question was solved under the condition that there are no three distinct sets such that A ∩ B ⊂ C.
KeywordsExtremal problem for families Sperner type theorem Forbidden subposet
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