Generalized balances in Sturmian words

@article{Fagnot2002GeneralizedBI,
  title={Generalized balances in Sturmian words},
  author={Isabelle Fagnot and Laurent Vuillon},
  journal={Discrete Applied Mathematics},
  year={2002},
  volume={121},
  pages={83-101}
}
One of the numerous characterizations of Sturmian words is based on the notion of balance. An innnite word x on the f0;1g alphabet is balanced if, given two factors of x, w and w 0 , having the same length, the diierence between the number of 0 0 s in w (denoted by jwj0) and the number of 0 0 s in w 0 is at most 1, i.e. jjwj0 ? jw 0 j0j 1. It is well known that an aperiodic word is Sturmian if and only if it is balanced. In this paper, the balance notion is generalized by considering the number… CONTINUE READING

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