On some generalizations of the Thue-Morse morphism
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. (C) 2002 Elsevier Science B.V. All rights reserved.
thue-morse arshon words overlap-free words overlap-free morphisms prouhet words