---
tag: QAE416GDEN
kind: concept
name: Square-free word
aliases: [cube-free-word, squarefree-word]
sources:
  - wikipedia: en:4088382@r1356229501
    locator: Square-free word
    note: adopted
    mention: wikipedia://en/4088382
    sections: [Summary]
same_as:
  wikidata: Q1138140
  wikipedia: Square-free word
inventory: [3B0069CQEF]
---

## Summary

In [[combinatorics|0JKW7W7XFR]], a **square-free word** is a word (a sequence of symbols) that does not contain any squares. A **square** is a word of the form $XX$, where $X$ is not empty. Thus, a square-free word can also be defined as a word that avoids the pattern $XX$.