Atoms of set systems with a fixed number of pairwise unions
type: Item
instance of: scholarly article
title: Atoms of set systems with a fixed number of pairwise unions
zbMATH Open document ID: 0854.05099
DOI: 10.1016/0012-365X(95)00184-X
published in: Discrete Mathematics
publication date: 1996-07-02T00:00:00Z
review text: Let \(H\) be a system of \(k\) sets with \(u\) pairwise unions, where \(u= (\begin{smallmatrix} t\\ 2\end{smallmatrix})+ \ell+ 1\) and \(0\leq \ell< t\leq k- 1\). The sharp bounds on the number of atoms \(k+ 2^t+ 2^\ell- t\) (for \(t\leq k- 2\)) and \(2^t+ 2^{\ell+ 1}\) (for \(t\neq k- 1\)) are proved.
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 895996
zbMATH Keywords: set systems
zbMATH Keywords: number of atoms
author: Penny Haxell
reviewed by: Péter Komjáth
MaRDI profile type: Publication
cites work: Q5653952
cites work: Q3693528
cites work: Union-free families of sets and equations over fields
cites work: Q3215325
cites work: Q3027106
cites work: Q3976643
full work available at URL: 0012-365x(95)00184-x
OpenAlex ID: W1978084087
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description: scientific article; zbMATH DE number 895996