Improved Lower Bound for Frankl's Union-Closed Sets Conjecture
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913419647516672 |
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| author | Alweiss, Ryan Huang, Brice Sellke, Mark |
| author_facet | Alweiss, Ryan Huang, Brice Sellke, Mark |
| contents | We verify an explicit inequality conjectured recently by Gilmer, thus proving that for any nonempty union-closed family $F \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $F$. One case, an explicit one-variable inequality, is checked by computer calculation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_11731 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Improved Lower Bound for Frankl's Union-Closed Sets Conjecture Alweiss, Ryan Huang, Brice Sellke, Mark Combinatorics We verify an explicit inequality conjectured recently by Gilmer, thus proving that for any nonempty union-closed family $F \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $F$. One case, an explicit one-variable inequality, is checked by computer calculation. |
| title | Improved Lower Bound for Frankl's Union-Closed Sets Conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2211.11731 |