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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.23986 |
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| _version_ | 1866917438959910912 |
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| author | Du, Longma Hu, Xinyu Liu, Ruilong Wang, Guanghui |
| author_facet | Du, Longma Hu, Xinyu Liu, Ruilong Wang, Guanghui |
| contents | The Ramsey number $r_k(s,n)$ is the smallest integer $N$ such that every $N$-vertex $k$-graph contains either a copy of $K_s^{(k)}$ or an independent set of size $n$. We prove that $r_4(5,n)\ge 2^{2^{cn^{1/7}}}$, where $c>0$ is an absolute constant. As a consequence, we determine the tower growth rate of $r_k(k+1,n)$, which completely solves the problem of establishing the tower growth rate for all classical off-diagonal hypergraph Ramsey numbers, first posed by Erdős and Hajnal in 1972. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23986 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A double-exponential lower bound for $r_4(5,n)$ Du, Longma Hu, Xinyu Liu, Ruilong Wang, Guanghui Combinatorics The Ramsey number $r_k(s,n)$ is the smallest integer $N$ such that every $N$-vertex $k$-graph contains either a copy of $K_s^{(k)}$ or an independent set of size $n$. We prove that $r_4(5,n)\ge 2^{2^{cn^{1/7}}}$, where $c>0$ is an absolute constant. As a consequence, we determine the tower growth rate of $r_k(k+1,n)$, which completely solves the problem of establishing the tower growth rate for all classical off-diagonal hypergraph Ramsey numbers, first posed by Erdős and Hajnal in 1972. |
| title | A double-exponential lower bound for $r_4(5,n)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.23986 |