A note on hypergraph extensions of Mantel's theorem

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