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arXiv · 2505.11373

A note on hypergraph extensions of Mantel's theorem

Jie Ma·Tianming Zhu
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Abstract

Chao and Yu introduced an entropy method for hypergraph Turán problems, and used it to show that the family of $\lfloor k/2\rfloor$ $k$-uniform tents have Turán density $k!/k^k$. Il'kovič and Yan improved this by reducing to a subfamily of $\lceil k/e\rceil$ tents. In this note, enhancing Il'kovič-Yan's result, we give a significantly shorter entropy proof, with optimal bounds within this framework.

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Jie Ma, Tianming Zhu. 2025-05-19. A note on hypergraph extensions of Mantel's theorem. https://arxiv.org/abs/2505.11373

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