Schur-convex functions

Schur-convex functions are a class of functions that preserve a specific type of ordering called majorization. If one set of numbers is more spread out or "unequal" than another, a Schur-convex function will assign a larger value to the more unequal set. Conversely, Schur-concave functions do the opposite. These functions are useful in various fields like economics and inequalities, as they help compare distributions and assess how the variation among elements affects the overall value, emphasizing the importance of fairness or inequality in the data.