---
tag: 1NXA9ARQD6
kind: concept
name: Place-permutation action
sources:
  - wikipedia: en:43583184@r1178312647
    locator: Place-permutation action
    note: adopted
    mention: wikipedia://en/43583184
    sections: [Summary]
same_as:
  wikidata: Q18388819
  wikipedia: Place-permutation action
inventory: [G4B3DS47F2]
---

## Summary

In mathematics, there are two natural interpretations of the **place-permutation action** of [[symmetric groups|0515A6D2Y1]], in which the group elements act on positions or *places*. Each may be regarded as either a left or a right action, depending on the order in which one chooses to compose [[permutations|05RWFKVTJ7]]. There are just two interpretations of the meaning of "acting by a permutation $\sigma$" but these lead to four variations, depending whether maps are written on the left or right of their arguments. The presence of so many variations often leads to confusion. When regarding the group algebra of a symmetric group as a *diagram algebra* it is natural to write maps on the right so as to compute compositions of diagrams from left to right.