Intersection Statements for Systems of Sets

W. A. Deuber, P. Erdos, D. S. Gunderson, A. V. Kostochka, A. G. Meyer

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Abstract

A family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(n, r) the most number of subsets of ann-element set which do not contain aΔ-system consisting ofrsets. Constructive new lower bounds forF(n, r) are given which improve known probabilistic results, and a new upper bound is given by employing an argument due to Erdos and Szemerédi. Another construction is given which shows that for certainn,F(n, 3)≥1.551n-2. We also show a relationship between the upper bound forF(n, 3) and the Erdos-Rado conjecture on the largest uniform family of sets not containing aΔ-system.

Original languageEnglish
Pages (from-to)118-132
Number of pages15
JournalJournal of Combinatorial Theory. Series A
Volume79
Issue number1
DOIs
Publication statusPublished - Jul 1 1997

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

Deuber, W. A., Erdos, P., Gunderson, D. S., Kostochka, A. V., & Meyer, A. G. (1997). Intersection Statements for Systems of Sets. Journal of Combinatorial Theory. Series A, 79(1), 118-132. https://doi.org/10.1006/jcta.1997.2778