elementary symmetric polynomial

The *elementary symmetric polynomial* on $n$ variables $\{X_i\}$ of degree $k \leq n$ is the polynomial

$\sigma_k(X_1, \cdots, X_n)
\coloneqq
\sum_{1 \leq i_1 \leq \cdots \leq i_k \leq n}
X_{i_1} \cdots X_{i_k}
\,.$

Equivalently these are the degree-$k$ summands in the polynomial

$(1+X_1)(1+X_2) \cdots (1+X_n)$

These polynomials form a basis for the Lambda-ring of symmetric functions.

- The Chern classes are, under the splitting principle, elementary symmetric polynomials of the first Chern classes.

- Wikipedia,
*Elementary symmetric polynomial*

Created on March 29, 2014 at 03:32:54. See the history of this page for a list of all contributions to it.