Abstract:A density $\alpha\in [0, 1)$ is a jump for $r$ if there is some $c >0$ such that there does not exist a family of $r$-uniform hypergraphs with Turán density in $(\alpha, \alpha + c)$. Erdös conjectured that all $\alpha\in [0, 1)$ 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 $r = 3$.
From: Vaughn Komorech [view email]
[v1]
Tue, 11 Nov 2025 00:46:03 UTC (10 KB)
[v2]
Fri, 3 Jul 2026 16:26:43 UTC (11 KB)
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