2-Bases of quadruples

Z. Füredi, Gyula O H Katona

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let ℬ(n, ≤ 4) denote the subsets of [n]:=\{ 1, 2, \dots, n\} of at most 4 elements. Suppose that ℱ is a set system with the property that every member of ℬ can be written as a union of (at most) two members of ℱ. (Such an ℱ is called a 2-base of ℬ) Here we answer a question of Erdos proving that |ℱ|≥ 1+n+\binom{n}{2}- {4/3n}, and this bound is best possible for n ≥ 8.

Original languageEnglish
Pages (from-to)131-141
Number of pages11
JournalCombinatorics Probability and Computing
Volume15
Issue number1-2
DOIs
Publication statusPublished - Jan 2006

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Set Systems
Quadruple
Erdös
Union
Denote
Subset

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Statistics and Probability

Cite this

2-Bases of quadruples. / Füredi, Z.; Katona, Gyula O H.

In: Combinatorics Probability and Computing, Vol. 15, No. 1-2, 01.2006, p. 131-141.

Research output: Contribution to journalArticle

Füredi, Z. ; Katona, Gyula O H. / 2-Bases of quadruples. In: Combinatorics Probability and Computing. 2006 ; Vol. 15, No. 1-2. pp. 131-141.
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