Hypergraphs in which all disjoint pairs have distinct unions

Abstract

Let ℓ be a set-system ofr-element subsets on ann-element set,r≧3. It is proved that if |ℓ|>3.5\(\left( {\begin{array}{*{20}c} n \\ {r - 1} \\ \end{array} } \right)\) then ℓ contains four distinct membersA, B, C, D such thatAB=CD andAB=CD=0.

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Füredi, Z. Hypergraphs in which all disjoint pairs have distinct unions. Combinatorica 4, 161–168 (1984). https://doi.org/10.1007/BF02579216

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AMS subject classification (1980)

  • 05 A 05
  • 05 C 35
  • 05 C 65