A Bound of the Cardinality of Families not Containing Δ-Systems
P. Erdős and R. Rado defined a Δ-system as a family in which every two members have the same intersection. Here we obtain a new upper bound of the maximum cardinality φ(n) of an n-uniform family not containing any Δ-system of cardinality 3. Namely, we prove that for any α > 1, there exists C = C(α) such that for any n, φ(n) ≤ C n!α−n .
KeywordsGreedy Algorithm Extremal Problem Minimum Cardinality Maximum Cardinality Preliminary Lemma
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- 1.P.Erdős, Problems and results on set systems and hypergraphs, Extended Abstrect, Conf.on Extremal Problems for Finite Sets, 1991, Visegrad, Hungary 1991, 85–92.Google Scholar