Geodesic
Union-closed families with small average overlap densities
David Ellis1
1University of Bristol
The electronic journal of combinatorics, Tome 29 (2022) no. 1

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Zbl DOI arXiv
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 $n$.
DOI : 10.37236/10121
Classification : 05D05
Mots-clés : union-closed conjecture, average overlap density

David Ellis  1

1 University of Bristol 
David Ellis. Union-closed families with small average overlap densities. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/10121
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     journal = {The electronic journal of combinatorics},
     year = {2022},
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     number = {1},
     doi = {10.37236/10121},
     zbl = {1481.05151},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10121/}
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