Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.07715 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911259003191296 |
|---|---|
| author | Komorech, Vaughn |
| author_facet | Komorech, Vaughn |
| contents | A density $α\in [0, 1)$ is a jump for $r$ if there is some $c >0$ such that there does not exist a family of $r$-uniform hypergraphs $\mathcal{F}$ with Turán density $π(\mathcal{F})$ in $(α, α+ c)$. Erdös conjectured that all $α\in [0, 1)$ are jumps for any $r$. This was disproven by Frankl and Rödl when they provided examples of non-jumps. In this paper, we provide a method for finding non-jumps for $r = 3$ using patterns. As a direct consequence, we find a few more examples of non-jumps for $r = 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-jumps of hypergraphs Komorech, Vaughn Combinatorics A density $α\in [0, 1)$ is a jump for $r$ if there is some $c >0$ such that there does not exist a family of $r$-uniform hypergraphs $\mathcal{F}$ with Turán density $π(\mathcal{F})$ in $(α, α+ c)$. Erdös conjectured that all $α\in [0, 1)$ are jumps for any $r$. This was disproven by Frankl and Rödl when they provided examples of non-jumps. In this paper, we provide a method for finding non-jumps for $r = 3$ using patterns. As a direct consequence, we find a few more examples of non-jumps for $r = 3$. |
| title | Non-jumps of hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.07715 |