A bound of the cardinality of families not containing Δ-Systems

Research output: Chapter in Book/Report/Conference proceedingChapter


P. Erdős and R. Rado defined a Δ-system as a family in which every two members have the same intersection. Here we obtain a new upper bound of the maximum cardinality φ(n) of an n-uniform family not containing any Δ-system of cardinality 3. Namely, we prove that for any α > 1, there exists C = C(α) such that for any n, φ(n)≤Cn!α−n.

Original languageEnglish (US)
Title of host publicationThe Mathematics of Paul Erdos II, Second Edition
Number of pages8
ISBN (Electronic)9781461472544
ISBN (Print)9781461472537
StatePublished - Jan 1 2013
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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