A characterization of overlap-free morphisms
Discrete Applied Mathematics
Subword complexity of a generalized Thue-Morse word
Information Processing Letters
Characterization of test-sets for overlap-free morphisms
Discrete Applied Mathematics
Lyndon factorization of the Prouhet words
Theoretical Computer Science - WORDS
Overlap-free morphisms and finite test-sets
Discrete Applied Mathematics
Aperiodicity Measure for Infinite Sequences
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
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In 1912, the Norwegian mathematician Axel Thue was the first to describe an overlap-free binary infinite word. This word was generated by a morphism which is called, since the works of Morse, the Thue-Morse morphism. Here, we present two generalizations of the Thue-Morse morphism in the case of alphabets with more than two letters. The extension of the characteristic properties of the word of Thue to the words generated by these morphisms is considered. One of these generalizations corresponds to the construction of Prouhet and a link with the Arshon words is given. In particular, we prove that if n is an even number then the n-letter Arshon word is generated by morphism.