Mapping words to powers by morphisms

📝 Original Info

• Title: Mapping words to powers by morphisms
• ArXiv ID: 2503.00960
• Date: 2025-03-02
• Authors: ** (논문에 명시된 저자 정보가 제공되지 않아 현재 확인 불가. 원문을 참고하시기 바랍니다.) **

📝 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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