Name
Abstract | ||
|---|---|---|
For a property Γ and a family of sets F, let f(F,Γ) be the size of the largest subfamily of F having property Γ. For a positive integer m, let f(m,Γ) be the minimum of f(F,Γ) over all families of size m. A family F is said to be Bd-free if it has no subfamily F′={FI:I⊆[d]} of 2d distinct sets such that for every I,J⊆[d], both FI∪FJ=FI∪J and FI∩FJ=FI∩J hold. A family F is a-union free if F1∪⋯∪Fa≠Fa+1 whenever F1,…,Fa+1 are distinct sets in F. We verify a conjecture of Erdős and Shelah that f(m,B2-free)=Θ(m2/3). We also obtain lower and upper bounds for f(m,Bd-free) and f(m,a-union free). |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.endm.2011.09.017 | Electronic Notes in Discrete Mathematics |
Keywords | DocType | Volume |
extremal set theory,union-free subfamilies,Bd-free subfamilies | Journal | 38 |
Issue | ISSN | Citations |
1 | 1571-0653 | 0 |
PageRank | References | Authors |
0.34 | 2 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| János Barát | 1 | 141 | 14.18 |
| Zoltán Füredi | 2 | 1237 | 233.60 |
| Ida Kantor | 3 | 6 | 2.76 |
| Younjin Kim | 4 | 7 | 2.64 |
| Balázs Patkós | 5 | 85 | 21.60 |