Extremal problems among subsets of a set
type: Item
instance of: scholarly article
title: Extremal problems among subsets of a set
zbMATH Open document ID: 0281.04002
DOI: 10.1016/0012-365X(74)90140-X
author: Daniel J. Kleitman
author: P. Erdős
published in: Discrete Mathematics
publication date: 1974-01-01T00:00:00Z
review text: This paper is a review of results and progress in the study of extremal problems on collection of subsets of a finite set, as of the spring of 1970, as presented at the 1970 Chapel Hill Conference. A typical problem might be given a collection of subsets of an \(n\) element set such that no two members have exactly \(k\) or fewer elements in common, how large can the collection be? Much has been accomplished in this area since 1970. A more recent review is contained in the article by \textit{G.O.H.Katona} in Combinatorics, Part 2 , Proc. Adv. Stud. Inst., Breukelen, 13-42 (1974; Zbl 0298.05142) on Extremal problems for hypergraphs; a paper by \textit{C. Greene} and \textit{D.J.Kleitman} in MAA Studies in Mathematics 17, Stud. in Combinatorics 22-79 (1978; Zbl 0409.05012) reviews some of the methods that have been developed for such problems.
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 05-02
zbMATH DE Number: 3440439
MaRDI profile type: Publication
cites work: Some Remarks on a Combinatorial Theorem of Erdös and Rado
cites work: Q5611031
cites work: Intersection theorems for systems of sets
cites work: Algebraic coding theory
cites work: On a combinatorial problem. II
cites work: On A Combinatorial Problem III
cites work: INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
cites work: Intersection Theorems for Systems of Sets
cites work: Intersection theorems for systems of finite sets
cites work: Q5518399
cites work: Q4071752
cites work: Q5680131
cites work: On a lemma of Littlewood and Offord on the distribution of certain sums
cites work: Families of Non-disjoint subsets
cites work: On a combinatorial conjecture of Erdös
cites work: Q5542810
cites work: On families of subsets of a finite set containing no two disjoint sets and their union
cites work: On a conjecture of milner on k-graphs with non-disjoint edges
cites work: On subsets contained in a family of non-commensurable subsets of a finite set
cites work: On Dedekind's Problem: The Number of Monotone Boolean Functions
cites work: Q5726070
cites work: A short proof of Sperner's lemma
cites work: Generalization of Sperner’s Theorem on the Number of Subsets of a Finite Set
cites work: SOME INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
cites work: A Combinatorial Theorem on Systems of Sets
cites work: Ein kombinatorisches Problem von P. Erdős und A. Hajnal
full work available at URL: 0012-365x(74)90140-x
OpenAlex ID: W2131114615
description: scientific article; zbMATH DE number 3440439