A Bound of the Cardinality of Families Not Containing $$\Delta $$ -Systems

Alexandr V. Kostochka
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Alexandr V. Kostochka: Russian Academy of Sciences, Institute of Mathematics, Siberian Branch

A chapter in The Mathematics of Paul Erdős II, 2013, pp 199-206 from Springer

Abstract: Summary P. Erdős and R. Rado defined a $$\Delta $$ -system as a family in which every two members have the same intersection. Here we obtain a new upper bound of the maximum cardinality $$\varphi (n)$$ of an n-uniform family not containing any $$\Delta $$ -system of cardinality 3. Namely, we prove that for any α > 1, there exists C = C(α) such that for any n, $$\displaystyle{\varphi (n) \leq Cn{!\alpha }^{-n}.}$$

Keywords: Maximum Cardinality; Disjoint Finite Sets; Main Construction; Preliminary Lemmas; Intersects (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7254-4_15

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

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