### Lecutre 6: Add example for El. Symm. Func. on 3 variables.

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 ... ... @@ -47,7 +47,18 @@ in general we have *Remark.* Note the strict inequalities between the inner indexes. The \$x_i\$'s are distinct. Their name stems from the fact, that owing to the nature of the product form \$\prod _{k=1} ^n (Z-X_k)\$, the \$e_k\$'s are invariant under permutation of the variables. That is \$e_k (X_1, \ldots, X_n) = e_k (X_\sigma(1), \ldots, X_\sigma(n))\$ for \$\sigma \in S_n\$. **Example.** (Elementary symmetric Functions on 3 variables) \begin{gather*} \begin{cases} e_0 = 1 \\ e_1 = X + Y + Z \\ e_2 = XY + XZ + YZ \\ e_3 = XYZ \end{cases} \end{gather*} Their name stems from the fact, that owing to the nature of the product form \$\prod _{k=1} ^n (Z-X_k)\$, the \$e_k\$'s are invariant under permutation of the variables. That is \$e_k (X_1, \ldots, X_n) = e_k (X_{\sigma(1)}, \ldots, X_{\sigma(n)})\$ for \$\sigma \in S_n\$. \subsectionmark{\textit{Lecture 6}} ## The extension over Elementary Symmetric Functions ... ...
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