About some Overlap-Free Morphisms on a n-Letter Alphabet
Patrice Séébold · Journal of automata, languages and combinatorics · 2002
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 study morphisms, generalizing the Thue-Morse morphism in the case of alphabets with more than two letters, which are obtained from a construction made by Prouhet in 1851. We examine in which case these morphisms are overlap-free and prove that the Prouhet words they generate are rigid. We also give a link with the construction realized by Arshon in 1937, proving in particular that the $n$-letter Arshon word is generated by morphism if and only if $n$ is an even number. These words are also rigid.