3 problems

Let $R=\{(\alpha,\beta,\gamma)\in[0,1]^3:\alpha\beta+\gamma>1,\alpha\gamma+\beta>1,\beta\gamma+\alpha>1\}$, and let … Define…

Let $k\geq 2$ and let $n$ be sufficiently large. For $1\geq\alpha,\beta,\gamma\geq 0$, an $(k,n)$-cyclic triple is a triple satisfying the six cyclic density inequalities stated in…

Let $\alpha,\beta,\gamma\in[0,1]$, let $R_2\subseteq[0,1]^3$ be the second region defined in the paper, and let $H_9$ be the specified tripartite graph. For a weighting $w$,…