Sunflower Bound with a Sub-Logarithmic Base
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912742123765760 |
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| author | Fukuyama, Junichiro |
| author_facet | Fukuyama, Junichiro |
| contents | We show that a family $\mathcal{F}$ of sets each of cardinality $m \in \mathbb{Z}_{>2}$ includes a $k$-sunflower if $ |\mathcal{F}| \ge \left( \frac{c k^2 \ln m}{\ln \ln m} \right)^m$ for some constant $c>0$, where $k$-sunflower means a family of $k$ different sets with a common pairwise intersection. The base of the exponential lower bound is sub-logarithmic for each $k$ updating the current best-known result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sunflower Bound with a Sub-Logarithmic Base Fukuyama, Junichiro Combinatorics 05D05 We show that a family $\mathcal{F}$ of sets each of cardinality $m \in \mathbb{Z}_{>2}$ includes a $k$-sunflower if $ |\mathcal{F}| \ge \left( \frac{c k^2 \ln m}{\ln \ln m} \right)^m$ for some constant $c>0$, where $k$-sunflower means a family of $k$ different sets with a common pairwise intersection. The base of the exponential lower bound is sub-logarithmic for each $k$ updating the current best-known result. |
| title | Sunflower Bound with a Sub-Logarithmic Base |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2510.19037 |