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Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable

Author Matthieu Rosenfeld

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Matthieu Rosenfeld

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Matthieu Rosenfeld. Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 81:1-81:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.MFCS.2016.81

Abstract

We show that every binary pattern of length greater than 14 is abelian-2-avoidable. The best known upper bound on the length of abelian-2-unavoidable binary pattern was 118, and the best known lower bound is 7. We designed an algorithm to decide, under some reasonable assumptions, if a morphic word avoids a pattern in the abelian sense. This algorithm is then used to show that some binary patterns are abelian-2-avoidable. We finally use this list of abelian-2-avoidable pattern to show our result. We also discuss the avoidability of binary patterns on 3 and 4 letters.
Keywords
  • combinatorics on words
  • pattern avoidance
  • abelian repetitions

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