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Sequences with constant number of return words

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Abstract

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.

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Authors and Affiliations

  1. Doppler Institute for Mathematical Physics and Applied Mathematics, and Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00, Prague 2, Czech Republic

    L’ubomíra Balková & Edita Pelantová

  2. LIAFA, CNRS, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Wolfgang Steiner

Authors
  1. L’ubomíra Balková
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  2. Edita Pelantová
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  3. Wolfgang Steiner
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Correspondence to Wolfgang Steiner.

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Balková, L., Pelantová, E. & Steiner, W. Sequences with constant number of return words. Monatsh Math 155, 251–263 (2008). https://doi.org/10.1007/s00605-008-0001-2

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  • DOI: https://doi.org/10.1007/s00605-008-0001-2

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