Pairwise intersections and forbidden configurations
type: Item
instance of: scholarly article
title: Pairwise intersections and forbidden configurations
zbMATH Open document ID: 1104.05068
author: Peter Keevash
author: R. P. Anstee
published in: European Journal of Combinatorics
publication date: 2006-11-15T00:00:00Z
review text: This interesting paper proves at first a strong stability version of the celebrated complete intersection theorem of Ahlswede and Khachatrian in the spirit of the Hilton-Milner theorem. Then using it the authors prove the following result: let \(f_m(a,b,c,d)\) denote the maximum size of a family of an \(m\)-element underlying set with the property that for all pairs \(A,B\) we have \(| A \cap B| \geq a,\) \(| \overline{A} \cap B| \geq b,\) \(| A \cap \overline{B}| \geq c\) and \(| \overline{A} \cap \overline{B}| \geq d.\) Then \(f_m(a,b,c,d) = \Theta( m^{a+b-1})\) for a wide range of the parameters.
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 5072610
zbMATH Keywords: Erdős-Ko-Rado theorem
zbMATH Keywords: Complete Intersection Theorem
zbMATH Keywords: conjecture of Anstee and Sali
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
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DOI: 10.1016/J.EJC.2006.05.002
description: scientific article; zbMATH DE number 5072610