Abstract
Peter Roth proved that there are no binary patterns of length six or more that are unavoidable on the two-letter alphabet. He gave an almost complete description of unavoidable binary patterns. In this paper we prove one of his conjectures: the pattern α2 β2 α is 2-avoidable. From this we deduce the complete classification of unavoidable binary patterns. We also study the concept of avoidability by iterated morphisms and prove that there are a few 2-avoidable patterns which are not avoided by any iterated morphism.
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Cassaigne, J. Unavoidable binary patterns. Acta Informatica 30, 385–395 (1993). https://doi.org/10.1007/BF01209712
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DOI: https://doi.org/10.1007/BF01209712