## Unavoidable binary patterns.(English)Zbl 0790.68096

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.

### MSC:

 68R15 Combinatorics on words
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### References:

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