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Sequences with constant number of return words |
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| Authors: | L’ubomíra Balková Edita Pelantová Wolfgang Steiner |
| Institution: | 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 2. LIAFA, CNRS, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France |
| 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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