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 language||English (US)|
|Title of host publication||The Mathematics of Paul Erdos II, Second Edition|
|Publisher||Springer New York|
|Number of pages||8|
|State||Published - Jan 1 2013|
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