The Lexicographically Least Binary Rich Word Achieving the Repetition Threshold

TL;DR

This paper identifies the lexicographically smallest infinite binary rich word that reaches a specific critical exponent, contributing to the understanding of combinatorial properties of binary words.

Contribution

It introduces the first construction of the lexicographically least infinite binary rich word with a given critical exponent.

Findings

The critical exponent of the word is $2+\sqrt{2}/2$

The word is the lexicographically least with this property

Provides insights into the structure of rich binary words

Abstract

We find the lexicographically least infinite binary rich word having critical exponent $2+\sqrt{2}/2$