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elementary symmetric polynomial
The coefficient of $x^{{nk}}$ in the polynomial $(x+t_{1})(x+t_{2})\cdots(x+t_{n})$ is called the $k^{\mathrm{th}}$ elementary symmetric polynomial in the $n$ variables $t_{1},\dots,t_{n}$. The elementary symmetric polynomials can also be constructed by taking the sum of all possible degree $k$ monomials in $t_{1},\dots,t_{n}$ having distinct factors.
The first few examples are:
 $n=1$:

$\begin{array}[]{l}t_{1}\end{array}$
 $n=2$:

$\begin{array}[]{l}t_{1}+t_{2}\\ t_{1}t_{2}\end{array}$
 $n=3$:

$\begin{array}[]{l}t_{1}+t_{2}+t_{3}\\ t_{1}t_{2}+t_{2}t_{3}+t_{1}t_{3}\\ t_{1}t_{2}t_{3}\end{array}$
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