Unverified Commit 7f2ab968 authored by rrueger's avatar rrueger
Browse files

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

parent 45ffe9db
No preview for this file type
......@@ -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
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment