Year: 2024
Type: article
Abstract: We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by 10 and this bound is optimal, extending a result of Rampersad, who proved that the bound 9 holds for the Fibonacci word. We then give a general result showing that for every e ∈ [ 1 , ( 5 + 5 ) / 2 ) there is a natural number N , depending only on e , such that every Sturmian word has the property that the distance between consecutive ending positions of e -powers occurring in the word is uniformly bounded by N .
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.644
Authors: Jason Bell, Chris Schulz, Jeffrey Shallit
Institution: University of Waterloo
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404061784