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Maximize multilinear sum

Source: 2015 ISL A3

July 7, 2016
inequalitiesalgebraIMO Shortlistmultivariate polynomialmaximizationn-variable inequality

Problem Statement

Let nn be a fixed positive integer. Find the maximum possible value of ∑1≤r<s≤2n(s−r−n)xrxs, \sum_{1 \le r < s \le 2n} (s-r-n)x_rx_s, where −1≤xi≤1-1 \le x_i \le 1 for all i=1,⋯ ,2ni = 1, \cdots , 2n.
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