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Generalization of elementary symmetric polynomials

The elementary symmetric polynomials (ESPs) are defined as - \begin{align*} E_{1}^{1} &= X_1, \\ E_{1}^{2} &= X_1 + X_2, \\ E_{2}^{2} &= X_1 X_2, \\ E_{2}^{3} &= X_1 X_2 + X_1 X_3 + X_2 X_3, \\ E_{k …
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