An intersection theorem for systems of sets

Research output: Contribution to journalArticlepeer-review

Abstract

Erdos and Rado defined a Δ-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality φ(n, q) of an n-uniform family not containing any Δ-system of cardinality q. Namely, we prove that, for any α > 1 and q, there exists C = C(α, q) such that, for any n, φ(n, q) ≤ Cn!((log log log n)2/α log log n)n.

Original languageEnglish (US)
Pages (from-to)213-221
Number of pages9
JournalRandom Structures and Algorithms
Volume9
Issue number1
DOIs
StatePublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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