On the structure of bispecial Sturmian words

作者：

Highlights：

• We extend a classical result of J. Berstel and A. de Luca stating that strictly bispecial Sturmian words are the maximal internal factors of primitive Christoffel words.

• Our extension shows that bispecial Sturmian words are the maximal internal factors of all Christoffel words.

• We give an enumerative formula for the number of bispecial Sturmian words of a given length.

• We study the minimal forbidden words for the language of finite Sturmian word.

摘要

•We extend a classical result of J. Berstel and A. de Luca stating that strictly bispecial Sturmian words are the maximal internal factors of primitive Christoffel words.•Our extension shows that bispecial Sturmian words are the maximal internal factors of all Christoffel words.•We give an enumerative formula for the number of bispecial Sturmian words of a given length.•We study the minimal forbidden words for the language of finite Sturmian word.

论文关键词：Sturmian words,Christoffel words,Special factors,Minimal forbidden words,Enumerative formula

论文评审过程：Received 1 January 2013, Revised 21 September 2013, Accepted 1 November 2013, Available online 19 November 2013.

论文官网地址：https://doi.org/10.1016/j.jcss.2013.11.001