For each $\alpha$ > 2 there is an infinite binary word with critical exponent $\alpha$

TL;DR

This paper proves that for every real number greater than 2, there exists an infinite binary word with a critical exponent exactly equal to that number, expanding understanding of combinatorial properties of binary sequences.

Contribution

It establishes the existence of infinite binary words with any prescribed critical exponent greater than 2, a new result in combinatorics on words.

Findings

Existence of binary words with critical exponent $orall \, ext{α} > 2$

Construction methods for such words

Implications for combinatorics and formal language theory

Abstract

For each $\alpha > 2$ there is a binary word with critical exponent $\alpha$.