Avoidable binary patterns in partial words (Q766156)

The classification of all binary patterns according to partial word avoidability is obtained in this very interesting paper. A new terminology on unavoidable patterns is introduced in order to include some undefined positions called holes. Using iterated morphisms, the construction of binary partial words with infinitely many holes avoiding certain patterns becomes possible. Then the authors prove that all binary patterns 2-avoidable in full words are also non-trivially 2-avoidable in partial words. Hence, the final result presents the characterization of all binary patterns in terms of avoidability in partial words.