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Mirzakhani and Vondr\\' ak showed that the greedy coloring of $H^{\\mathrm{Id}}_{k,q}$ produces the maximal number of monochromatic hyperedges. The line graph of $H_{k,q}^\\pi$ is built from the copies of the graph $G_\\pi$ that represents which subsets of consecutive numbers of $[k-1]$ are contiguous in $\\pi$. 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