2026-07-21T19:27:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6489 2024-03-06T10:38:25Z ddc:004 open_access

Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable Rosenfeld, Matthieu combinatorics on words pattern avoidance abelian repetitions 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Matthieu Rosenfeld 2016 Is Part Of LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2016.81 urn:nbn:de:0030-drops-64892 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.81 eng https://creativecommons.org/licenses/by/3.0/legalcode