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Mapping words to powers by morphisms

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arxiv 2503.00960 v1 pith:Y4SABCAZ submitted 2025-03-02 cs.FL math.CO

classification cs.FLmath.CO
keywords mappedwordwordsbounddecidinggivenmorphismmorphisms
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mapped Exponent and Asymptotic Critical Exponent of Words

    math.CO 2025-06 conditional novelty 7.0 of 10

    The paper classifies which words become arbitrarily repetitive under injective morphisms and shows the asymptotic critical exponent of binary words cannot be raised by one or more.

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