Publication date
April 2007
DOI Publisher
Elsevier Ltd. ISSN
0195-6698 Citation count (estimate)
36Abstract
AbstractDejean conjectured that the repetition threshold of a k-letter alphabet is k/(k−1),k≠3,4. Values of the repetition threshold for k<5 were found by Thue, Dejean and Pansiot. Moulin-Ollagnier attacked Dejean’s conjecture for 5≤k≤11. Building on the work of Moulin-Ollagnier, we propose a method for deciding whether a given Sturmian word with quadratic slope confirms the conjecture for a given k. Elaborating this method in terms of directive words, we develop a search algorithm for verifying the conjecture for a given k. An implementation of our algorithm gives suitable Sturmian words for 7≤k≤14. We prove that for k=5, no suitable Sturmian word exists
Add to ORKG