The Shortest Interesting Binary Words

TL;DR

This paper identifies two specific binary words of lengths 4 and 6 that are fundamental in various combinatorial problems, highlighting their significance across multiple research works.

Contribution

The paper introduces the concept of the shortest interesting binary words and demonstrates their importance in combinatorics on words.

Findings

Two binary words of lengths 4 and 6 are central to many combinatorial problems.

These words are frequently cited in combinatorics literature.

They serve as key examples in multiple research contexts.

Abstract

I will show that there exist two binary words (one of length 4 and one of length 6) that play a special role in many different problems in combinatorics on words. They can therefore be considered \textit{the shortest interesting binary words}. My claim is supported by the fact that these two words appear in dozens of papers in combinatorics on words.