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  "body": "\n## Summary\n\nA Schur-convex function is a function of $n$ real variables that preserves the order of [[majorization|5K7VT2VKZT]].\nIf $x$ is more spread out than $y$ and has the same sum, then $f(x) \\ge f(y)$ for a Schur-convex $f$.\nEvery symmetric convex function is Schur-convex, and many classical inequalities, such as [[Karamata's inequality|FWKSHEJ9RP]], are statements that some function is Schur-convex.\nThe [[definition|24CEMRAGJ8]] gives the precise condition.\n\n## Explanations\n\n### L1 human\n\nThink of a vector of $n$ numbers as a way to share a fixed total among $n$ people.\nOne sharing majorizes another when it is less equal.\nA Schur-convex function measures inequality: it grows when the sharing becomes less equal.\nFor example the largest entry $\\max_i x_i$ is Schur-convex: $(3, 0)$ is less equal than $(2, 1)$, and $3 \\ge 2$.\n",
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