---
tag: TJH5KEW8MJ
kind: concept
name: Permutation class
sources:
  - wikipedia: en:40940518@r1338623318
    locator: Permutation class
    note: adopted
    mention: wikipedia://en/40940518
    sections: [Summary]
same_as:
  wikidata: Q48995809
  wikipedia: Permutation class
inventory: [EK1BMJWKRC]
---

## Summary

In the study of [[permutations|05RWFKVTJ7]] and permutation patterns, a **permutation class** is a set $C$ of permutations for which every pattern within a permutation in $C$ is also in $C$. In other words, a permutation class is a hereditary property of permutations, or a downset in the permutation pattern order. A permutation class may also be known as a **pattern class**, **closed class**, or simply **class** of permutations.