Sharpness of some intersection theorems
type: Item
instance of: scholarly article
title: Sharpness of some intersection theorems
zbMATH Open document ID: 0971.05109
author: L. Spissich
author: Zsolt Tuza
author: Mihály Hujter
published in: European Journal of Combinatorics
publication date: 2001-10-30T00:00:00Z
review text: A theorem of \textit{P. Frankl} and \textit{I. G. Rosenberg} [A finite set intersection theorem, Eur. J. Comb. 2, 127-129 (1981; Zbl 0461.05001)] states: Let \(0\leq \mu_1< p\) be integers and let \({\mathcal F}\) be a family of \(k\)-element subsets of an \(n\)-element set such that \(k\not\equiv \mu_1\pmod p\) and \(|F\cap F'|\equiv \mu_1\pmod p\) for any two distinct members \(F\), \(F'\) of \({\mathcal F}\). Then \(|{\mathcal F}|\leq n\). The authors construct infinite sequences of non-trivial families for which the bound is attained. Some further constructions are given for related inequalities.
reviewed by: Konrad Engel
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1538573
zbMATH Keywords: Frankl-Wilson inequality
zbMATH Keywords: Frankl-Rosenberg inequality
zbMATH Keywords: Deza-Rosenberg inequality
zbMATH Keywords: Steiner system
zbMATH Keywords: intersection theorem
MaRDI profile type: Publication
full work available at URL: eujc.2000.0408
OpenAlex ID: W1988274492
cites work: Q3866159
cites work: A finite set intersection theorem
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cites work: Intersection theorems with geometric consequences
cites work: Q5585020
cites work: An existence theory for pairwise balanced designs. III: Proof of the existence conjectures
DOI: 10.1006/EUJC.2000.0408
description: scientific article; zbMATH DE number 1538573