3 problems

Let $r\geq 2$ be an integer and let $F$ be an $(r-1)$-graph. Let $F(t)$ denote the $r$-uniform hypergraph obtained by adjoining a new vertex to every edge of $F$, and let…

For each integer $r\geq 4$, let $C^{(r)}_{r\ell}$ denote the $r$-uniform tight cycle with $r\ell$ edges, and let $s(F)$ denote the Sidorenko exponent of a hypergraph $F$. Conjectur…

Let $C^{(3)}_{3\ell}$ denote the $3$-uniform tight cycle with $3\ell$ edges, and let $s(F)$ denote the Sidorenko exponent of a hypergraph $F$. Near-Sidorenko conjecture for 3-unifo…