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

$\begin{array}{c}{t}_{1}\hfill \end{array}$
 $n=2$:

$\begin{array}{c}{t}_{1}+{t}_{2}\hfill \\ {t}_{1}{t}_{2}\hfill \end{array}$
 $n=3$:

$\begin{array}{c}{t}_{1}+{t}_{2}+{t}_{3}\hfill \\ {t}_{1}{t}_{2}+{t}_{2}{t}_{3}+{t}_{1}{t}_{3}\hfill \\ {t}_{1}{t}_{2}{t}_{3}\hfill \end{array}$
Title  elementary symmetric polynomial 

Canonical name  ElementarySymmetricPolynomial 
Date of creation  20130322 12:09:01 
Last modified on  20130322 12:09:01 
Owner  djao (24) 
Last modified by  djao (24) 
Numerical id  9 
Author  djao (24) 
Entry type  Definition 
Classification  msc 05E05 