elementary symmetric polynomial

The coefficient of $x^{n-k}$ 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:

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

单词	ElementarySymmetricPolynomial
释义	elementary symmetric polynomial The coefficient of $x^{n-k}$ 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: $n=1$ : $\\begin{array}[]{l}t_{1}\\end{array}$ $n=2$ : $\\begin{array}[]{l}t_{1}+t_{2}\\\\t_{1}t_{2}\\end{array}$ $n=3$ : $\\begin{array}[]{l}t_{1}+t_{2}+t_{3}\\\\t_{1}t_{2}+t_{2}t_{3}+t_{1}t_{3}\\\\t_{1}t_{2}t_{3}\\end{array}$
随便看	regular elements of finite ring RegularExpression regular expression RegularGroupAction regular group action RegularIdeal regular ideal RegularityTheoremForTheLaplaceEquation regularity theorem for the Laplace equation RegularLanguage regular language RegularLocalRing regular local ring RegularlyOpen regularly open RegularMap regular map RegularMeasure regular measure RegularOpenAlgebra regular open algebra RegularOpenSet regular open set RegularPolygon regular polygon