Sequences with constant number of return words

@article{Balkov2006SequencesWC,
  title={Sequences with constant number of return words},
  author={L. Balkov{\'a} and E. Pelantov{\'a} and W. Steiner},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2006},
  volume={155},
  pages={251-263}
}
  • L. Balková, E. Pelantová, W. Steiner
  • Published 2006
  • Mathematics, Computer Science
  • Monatshefte für Mathematik
  • An infinite word has the property Rm if every factor has exactly m return words. Vuillon showed that R2 characterizes Sturmian words. We prove that a word satisfies Rm if its complexity function is (m − 1)n + 1 and if it contains no weak bispecial factor. These conditions are necessary for m = 3, whereas for m = 4 the complexity function need not be 3n + 1. A new class of words satisfying Rm is given. 

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