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  "body": "\n## Statement\n\nLet $r$ and $s$ be positive integers. Let $h_1, h_2, \\dots, h_r$ be integers with $h_i \\ge s$ for each $i = 1, \\dots, r$.\n\nThen there is a least positive integer $R(s : h_1, \\dots, h_r)$ with this property. Let $n \\ge R(s : h_1, \\dots, h_r)$. Colour every $s$-element subset of $\\{1, \\dots, n\\}$ with one of $r$ colours, in any way. Then there is a colour $\\alpha \\in \\{1, \\dots, r\\}$ and a set $H \\subseteq \\{1, \\dots, n\\}$ with $|H| = h_\\alpha$, such that every $s$-element subset of $H$ has colour $\\alpha$.\n\n## Remarks\n\nFor $s = 2$ the $s$-subsets are the edges of a complete graph, and the number is a generalised [[Ramsey number|01DSVCRF6X]] for $r$ colours.\n",
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  "name": "Ramsey's theorem for colourings of s-subsets with several colours",
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