English

Sequences with constant number of return words

Combinatorics 2007-09-27 v4 Discrete Mathematics

Abstract

An infinite word has the property RmR_m if every factor has exactly mm return words. Vuillon showed that R2R_2 characterizes Sturmian words. We prove that a word satisfies RmR_m if its complexity function is (m1)n+1(m-1)n+1 and if it contains no weak bispecial factor. These conditions are necessary for m=3m=3, whereas for m=4m=4 the complexity function need not be 3n+13n+1. New examples of words satisfying RmR_m are given by words related to digital expansions in real bases.

Keywords

Cite

@article{arxiv.math/0608603,
  title  = {Sequences with constant number of return words},
  author = {Lubomira Balkova and Edita Pelantova and Wolfgang Steiner},
  journal= {arXiv preprint arXiv:math/0608603},
  year   = {2007}
}
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