Unavoidable binary patterns
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 \(\alpha^ 2\beta^ 2\alpha\) 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.
scientific article; zbMATH DE number 567297