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 $⌊k/2⌋$ $k$-uniform tents have Turán density $k!/{k^k}$ . Il’kovič and Yan [5] improved this by reducing to a subfamily of ${\lceil}k/e⌉$ tents. In this note, enhancing Il’kovič-Yan’s result, we give a significantly shorter entropy proof, with optimal bounds within this framework.