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arXiv · 2511.07715

Non-jumping densities of 3-uniform hypergraphs

Vaughn Komorech
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Abstract

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 with Turán density 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 $r = 3$.

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Vaughn Komorech. 2026-07-03. Non-jumping densities of 3-uniform hypergraphs. https://arxiv.org/abs/2511.07715

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