---
tag: 0X5QVCF06N
kind: concept
name: Elementary symmetric polynomial
msc: ["05E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial
    locator: lead section
same_as:
  wikidata: Q2235316
  wikipedia: Elementary symmetric polynomial
---

## Summary

The elementary symmetric polynomials in $n$ variables are the sums of all products of $k$ distinct variables, for $k = 0, \dots, n$.
They generate all symmetric polynomials.
The [[definition of the elementary symmetric polynomials|0ZMY8441GW]] gives the formula.