---
tag: 02DKV69ZH0
kind: concept
name: Sign of a permutation
aliases: [signature-of-a-permutation]
msc: [20B30]
sources:
  - url: https://en.wikipedia.org/wiki/Parity_of_a_permutation
    locator: lead section
---

## Summary

The sign of a permutation is $+1$ or $-1$, according to the parity of the number of transpositions in a decomposition of the permutation.
The sign map is a homomorphism from $S_n$ to $\{1, -1\}$.