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The Complete Nontrivial-Intersection Theorem for Systems of Finite Sets

✍ Scribed by Rudolf Ahlswede; Levon H. Khachatrian

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
728 KB
Volume
76
Category
Article
ISSN
0097-3165

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✦ Synopsis

The authors have proved in a recent paper a complete intersection theorem for systems of finite sets. Now we establish such a result for nontrivial-intersection systems (in the sense of Hilton and Milner [Quart.

πŸ“œ SIMILAR VOLUMES

An intersection theorem for systems of s
An intersection theorem for systems of sets
✍ A. V. Kostochka πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 346 KB πŸ‘ 2 views

Erdos and Rado defined a A-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality q ( n , q ) of an n-uniform family not containing any A-system of cardinality q. Namely, we prove that, for any a > 1 and q , there exists