An intersection theorem for systems of sets
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Erdos and Rado defined a A-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality q ( n , q ) of an n-uniform family not containing any A-system of cardinality q. Namely, we prove that, for any a > 1 and q , there exists C = C(a, q ) such that, for any n ,
[1] Paul Erdös,et al. Extremal problems on graphs and hypergraphs , 1974 .
[2] J. Spencer. Intersection Theorems for Systems of Sets , 1977, Canadian Mathematical Bulletin.