Geodesic
Improved lower bound for Frankl's union-closed sets conjecture
Ryan Alweiss1 ; Brice Huang2 ; Mark Sellke3
1University of Cambridge
2MIT
3Harvard
The electronic journal of combinatorics, Tome 31 (2024) no. 3
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We verify an explicit inequality conjectured in [Gilmer, 2022, arXiv:2211.09055], thus proving that for any nonempty union-closed family $\mathcal{F} \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $\mathcal{F} \$. One case, an explicit one-variable inequality, is checked by computer calculation.
DOI : 10.37236/12232
Classification : 05D05, 05-08
Mots-clés : optimization over two point masses

Ryan Alweiss  1   ; Brice Huang  2   ; Mark Sellke  3

1 University of Cambridge
2 MIT
3 Harvard 
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Ryan Alweiss; Brice Huang; Mark Sellke. Improved lower bound for Frankl's union-closed sets conjecture. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12232

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