Completing a combinatorial proof of the rigidity of Sturmian words generated by morphisms
In [Theor. Comput. Sci. 195, No. 1, 91--109 (1998; Zbl 0981.68104); Lect. Notes Comput. Sci. 1113, 506--516 (1996; Zbl 0889.68094)], the second author proved that Sturmian words generated by morphisms are rigid. There was a gap in the proof; more precisely, in the property that two commuting morphisms \(f\), \(g\) generating the same Sturmian word such that \(f^m= g^n\) for some integers \(n\), \(m\) are necessarily powers of some Sturmian morphism \(h\). This property has to be proved. (The corresponding property for words, known as the Lyndon-Schützenberger theorem, uses the fact that the monoid of words on a finite alphabet is a free monoid.) The authors of the paper under review prove that property, thus filling the gap in the cited papers.
scientific article; zbMATH DE number 6039155