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 language English 131-141 11 Combinatorics Probability and Computing 15 1-2 https://doi.org/10.1017/S0963548305007248 Published - Jan 2006

Set Systems
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.
@article{67e48c562b5842d1938cc7fc6223dfde,
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.",
author = "Z. F{\"u}redi and Katona, {Gyula O H}",
year = "2006",
month = "1",
doi = "10.1017/S0963548305007248",
language = "English",
volume = "15",
pages = "131--141",
journal = "Combinatorics Probability and Computing",
issn = "0963-5483",
publisher = "Cambridge University Press",
number = "1-2",

}

TY - JOUR

AU - Füredi, Z.

AU - Katona, Gyula O H

PY - 2006/1

Y1 - 2006/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=29744434736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29744434736&partnerID=8YFLogxK

U2 - 10.1017/S0963548305007248

DO - 10.1017/S0963548305007248

M3 - Article

AN - SCOPUS:29744434736

VL - 15

SP - 131

EP - 141

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 1-2

ER -