Set systems with three intersections

Abstract

LetX be a finite set ofn elements and ℱ a family of 4a+5-element subsets,a≧6. Suppose that all the pairwise intersections of members of ℱ have cardinality 0,a or 2a+1. We show thatc 1 n 4/3<max |F|<c 2 n 4/3 for some positivec i’s. This answers a question of P. Frankl.

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Füredi, Z. Set systems with three intersections. Combinatorica 5, 27–31 (1985). https://doi.org/10.1007/BF02579439

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 65