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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.07715 |
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Table of 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 $r = 3$.