Let $r\geq3$ and $G$ be an $r$-uniform hypergraph with vertex set $\left\{ 1,\ldots,n\right\} $ and edge set $E$. Let \[ \mu\left( G\right) :=\max {\textstyle\sum\limits_{\left\{ i_{1},\ldots,i_{r}\right\} \in E}} x_{i_{1}}\cdots x_{i_{r}}, \] where the maximum is taken over all nonnegative $x_{1},\ldots,x_{n}$ with $x_{1}+\cdots+x_{n}=1.$ Let $t\geq r-1$ be the unique real number such that $\left\vert E\right\vert =\binom{t}{r}$... (read more)

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