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On set systems without weak 3-Δ-subsystems

✍ Scribed by M. Axenovich; D. Fon-Der-Flaass; A. Kostochka

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
226 KB
Volume
138
Category
Article
ISSN
0012-365X

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✦ Synopsis

A collection of sets is called a weak A-system if sizes of all pairwise intersections of these sets coincide. We prove a new upper bound on the function ./~,.(n), the maximal size of a collection of n-element sets no three of which form a weak A-system. Namely, we prove that, for every 6 > 0. L,(n) = o(n!1"2 +~).

📜 SIMILAR VOLUMES

On the Size of Set Systems on [n] Not Co
On the Size of Set Systems on [n] Not Containing Weak (r, Δ)-Systems
✍ Vojtěch Rödl; Luboš Thoma 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 286 KB

Let r 3 be an integer. A weak (r, 2)-system is a family of r sets such that all pairwise intersections among the members have the same cardinality. We show that for n large enough, there exists a family F of subsets of [n] such that F does not contain a weak (r, 2)-system and |F| 2 (1Â3) } n 1Â5 log