Length-k-overlap-free Binary Infinite Words

Authors:
Patrice Séébold
Affiliations:
(Correspd.) (Dep. Mathématiques et Informatique Appliquées, Univ. Montpellier and Laboratoire d'Informatique, de Robotique et de Micro-électronique de Montpellier, France) Univ. Mon ...
Venue:
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
Year:
2012

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Abstract

We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with |x| ≤ k − 1. We prove that no such word can be generated by a morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist length-k-overlap-free binary infinite words which are not length-(k − 1)-overlap-free. As an application, we prove that, for every non-negative integer n, there exist infinitely many length-k-overlap-free binary infinite partial words with n holes.