Mapping words to powers by morphisms

Aleksi Saarela

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arXiv · 2503.00960

Mapping words to powers by morphisms

Aleksi Saarela

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Abstract

We characterize the words that can be mapped to arbitrarily high powers by injective morphisms. For all other words, we prove a linear upper bound for the highest power that they can be mapped to, and this bound is optimal up to a constant factor if there is no restriction on the size of the alphabet. We also prove that, for any integer $n \geq 2$, deciding whether a given word can be mapped to an $n$th power by a nonperiodic morphism is NP-hard and in PSPACE, and so is deciding whether a given word can be mapped to a nonprimitive word by a nonperiodic morphism.

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BibTeX RIS

Aleksi Saarela. 2025-03-02. Mapping words to powers by morphisms. https://arxiv.org/abs/2503.00960

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