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

Alexandr V. Kostochka

doi:10.1007/978-1-4614-7254-4_15

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

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Abstract

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
Pages	199-206
Number of pages	8
ISBN (Electronic)	9781461472544
ISBN (Print)	9781461472537
DOIs	https://doi.org/10.1007/978-1-4614-7254-4_15
State	Published - Jan 1 2013
Externally published	Yes

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General Mathematics

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10.1007/978-1-4614-7254-4_15

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

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