Bounds on Maximal Families of Sets Not Containing Three Sets with A ∩ B ⊂ C, A ⊄ B |
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| Authors: | Teena Carroll Gyula O H Katona |
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| Institution: | (1) School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA;(2) Rényi Institute, Budapest, Hungary |
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| Abstract: | 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.
The second author was supported by the Hungarian National Foundation for Scientific Research grant numbers NK062321, AT048826,
the Bulgarian National Science Fund under Grant IO-03/2005 and the projects of the European Community: INTAS 04-77-7171, FIST–MTKD-CT-2004-003006. |
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| Keywords: | Extremal problem for families Sperner type theorem Forbidden subposet |
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