Concerning Kurosaki's squarefree word
Serina Camungol, Narad Rampersad
TL;DR
This paper proves that Kurosaki's infinite squarefree word over three letters also avoids certain fractional powers, specifically 7/4+-powers, confirming its optimality in pattern avoidance.
Contribution
It demonstrates that Kurosaki's construction not only produces squarefree words but also avoids 7/4+-powers, establishing optimal pattern avoidance over three-letter alphabets.
Findings
Kurosaki's word avoids 7/4+-powers.
The avoidance is proven to be optimal for three-letter alphabets.
The result extends the understanding of pattern avoidance in infinite words.
Abstract
In 2008, Kurosaki gave a new construction of a (bi-)infinite squarefree word over three letters. We show that in fact Kurosaki's word avoids 7/4+-powers, which, as shown by Dejean, is optimal over a 3-letter alphabet.
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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Finite Group Theory Research