Repetition-Free Words
Abstract Diamond Implementation Diamond Paper
Blanchet-Sadri Abraham Elara
ABSTRACT

We propose an algorithm that given as input a full word w of length n, and positive integers p and d, outputs (if any exists) a maximal p-periodic partial word contained in w with the property that no two holes are within distance d. Our algorithm runs in O(nd) time and is used for the study of freeness of partial words. Furthermore, we construct an infinite word over a five-letter alphabet that is overlap-free even after the insertion of an arbitrary number of holes, answering affirmatively a conjecture from Blanchet-Sadri, Mercas, and Scott.

Keywords: Combinatorics on words; Partial words; Freeness; Periodicity.



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Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. DMS-0754154. The Department of Defense is also gratefully acknowledged.
Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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