Union-closed families with small average overlap densities (Q2073302)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Union-closed families with small average overlap densities |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Union-closed families with small average overlap densities |
scientific article |
Statements
Union-closed families with small average overlap densities (English)
0 references
1 February 2022
0 references
Summary: In this very short paper, we show that the average overlap density of a union-closed family \(\mathcal{F}\) of subsets of \(\{1,2,\ldots,n\}\) may be as small as \[\Theta((\log_2 \log_2 |\mathcal{F}|)/(\log_2 |\mathcal{F}|)),\] for infinitely many positive integers \(n\).
0 references
union-closed conjecture
0 references
average overlap density
0 references
