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''f'' is Schur-convex if and only if
<math>(x_i - x_j)\left(\frac{\partial f}{\partial x_i} - \frac{\partial f}{\partial x_j}\right) \ge 0 </math> for all <math>x \in \mathbb{R}^d</math>
holds for all 1≤''i''≠''j''≤''d''.<ref>{{cite book|last1=E. Peajcariaac|first1=Josip|last2=L. Tong|first2=Y.|title=Convex Functions, Partial Orderings, and Statistical Applications|publisher=Academic Press|isbn=9780080925226|page=333}}</ref>
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