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Some properties of morphic images of (eventually) dendric words

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Abstract

The class of (eventually) dendric words generalizes well-studied families such as the Sturmian words, the Arnoux–Rauzy words or the codings of interval exchanges. Dendricity is also a particular case of neutrality. We show that, however, the notions of eventual dendricity and eventual neutrality coincide. This paper then focuses on two questions linking dendricity and morphisms. We first look at the evolution of the factor complexity when applying a non-erasing morphism to an eventually dendric word and show that it can only grow by an additive constant. We next generalize a result known for Sturmian words and consider the morphisms that preserve dendricity for all dendric words. We show that they correspond exactly to the morphisms generated by the Arnoux-Rauzy morphisms.

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Notes

  1. Note that this is not true if \(b' \ne c'\) and we are on an alphabet of size 2.

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Acknowledgements

The author is supported by an FNRS Research Fellow grant. The author would like to thank Julien Leroy for discussions about the results of this paper.

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  1. Department of Mathematics, University of Liège, Allée de la Découverte 12 (B37), 4000, Liège, Belgium

    France Gheeraert

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  1. France Gheeraert
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Correspondence to France Gheeraert.

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Communicated by H. Bruin.

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Gheeraert, F. Some properties of morphic images of (eventually) dendric words. Monatsh Math 202, 335–351 (2023). https://doi.org/10.1007/s00605-023-01877-4

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