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Maximum value, function of partition and its conjugate

Suppose that we have $n\in \mathbb{Z}_{+}$ and some $\alpha\ge 3$. I am trying to find maximum value of: $\sum_{i,j=1}^{n}|\lambda_{i}-\lambda_{j}^{*}|^{\alpha},$ over $\{\lambda\in \mathbb{Z}^...
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