Monatshefte für Mathematik

, 155:251 | Cite as

Sequences with constant number of return words

  • L’ubomíra Balková
  • Edita Pelantová
  • Wolfgang Steiner


An infinite word has the property R m if every factor has exactly m return words. Vuillon showed that R 2 characterizes Sturmian words. We prove that a word satisfies R m 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 R m is given.


Return words Complexity Special factors Sturmian words 

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • L’ubomíra Balková
    • 1
  • Edita Pelantová
    • 1
  • Wolfgang Steiner
    • 2
  1. 1.Doppler Institute for Mathematical Physics and Applied Mathematics, and Department of Mathematics, FNSPECzech Technical UniversityPrague 2Czech Republic
  2. 2.LIAFA, CNRSUniversité Paris Diderot-Paris 7Paris Cedex 13France

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