Contents

Definition

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.

References

Created on March 29, 2014 at 03:23:38. See the history of this page for a list of all contributions to it.