A note on hypergraph extensions of Mantel's theorem

TL;DR

This paper improves the entropy-based proof of a hypergraph Turán problem related to Mantel's theorem, providing a shorter proof with optimal bounds for a specific family of hypergraphs.

Contribution

It offers a significantly shorter entropy proof for the hypergraph Turán problem, achieving optimal bounds within the established framework.

Findings

Shorter entropy proof for hypergraph Turán problem

Optimal bounds for the family of  tents

Enhanced understanding of hypergraph extensions of Mantel's theorem

Abstract

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