Abelian returns in Sturmian words

作者：Puzynina Svetlana^*; Zamboni Luca Q

来源：Journal of Combinatorial Theory - Series A, 2013, 120(2): 390-408.

DOI：10.1016/j.jcta.2012.09.002

• Sturmian word
• Return word
• Abelian equivalence

Return words constitute a powerful tool for studying symbolic dynamical systems. They may be regarded as a discrete analogue of the first return map in dynamical systems. In this paper we investigate two abelian variants of the notion of return word, each of them gives rise to a new characterization of Sturmian words. We prove that a recurrent infinite word is Sturmian if and only if each of its factors has two or three abelian (or semi-abelian) returns. We study the structure of abelian returns in Sturmian words and give a characterization of those factors having exactly two abelian returns. Finally we discuss connections between abelian returns and periodicity in words.

• 出版日期2013-2