论文标题
关于arnoux-rauzy单词的刚性
On the rigidity of Arnoux-Rauzy words
论文作者
论文摘要
如果解决此词的所有替换是同一替代的权力，则由替代产生的无限词是僵化的。斯特里亚语单词以及特征性的arnoux-rauzy单词被称为僵化。在本文中，我们证明所有arnoux-rauzy单词都是僵化的。证明依赖于两种主要成分：首先，固定arnoux-rauzy单词的原始替代品具有共同的力量，其次，依代性episturmian替代的概念（即，固定arnoux-rauzy word的替代）的概念。主要难度是组合性质，并依赖于施加Episturmian取代的正常化过程：正方形的正常形式不一定等于正常形式的平方。
An infinite word generated by a substitution is rigid if all the substitutions which fix this word are powers of a same substitution. Sturmian words as well as characteristic Arnoux-Rauzy words are known to be rigid. In the present paper, we prove that all Arnoux-Rauzy words are rigid. The proof relies on two main ingredients: firstly, the fact that the primitive substitutions that fix an Arnoux-Rauzy word share a common power, and secondly, the notion of normal form of an episturmian substitution (i.e., a substitution that fixes an Arnoux-Rauzy word). The main difficulty is then of a combinatorial nature and relies on the normalization process when taking powers of episturmian substitutions: the normal form of a square is not necessarily equal to the square of the normal forms.
