A note on hypergraph extensions of Mantel's theorem

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.