Binary avoidability and Thue-Morse words
This paper studies properties of binary avoidability concerning the Thue-Morse sequence. This well-known sequence is defined on the alphabet \(\{a,b\}\) as the fixed point beginning by \(a\) of the substitution \(\sigma\): \(\sigma(a)= ab\), \(\sigma(b)= ba\). The Thue-Morse sequence is known to be strongly cubeless; i.e., to avoid words of the form \(xxx\) and \(xyxyx\), where \(x,y\) are defined on the alphabet \(\{a,b\}\). The paper under review sketches the proofs of the following two results: it first describes the set of all binary strongly cubeless words in terms of Thue-Morse words (i.e., the iterates under the Thue-Morse substitution of the letters \(a\) and \(b\)). Then a complete description of the ideal of the binary words avoided by the Thue-Morse words is given.
scientific article; zbMATH DE number 1122782