Mapped Exponent and Asymptotic Critical Exponent of Words

📝 Original Info

• Title: Mapped Exponent and Asymptotic Critical Exponent of Words
• ArXiv ID: 2506.04091
• Date: 2025-06-04
• Authors: ** 정보가 제공되지 않음 (논문에 명시된 저자 정보를 확인해 주세요.) **

📝 Abstract

We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and asymptotic critical exponents of infinite words. We characterize finite words that, when mapped by injective morphisms, can have arbitrarily high fractional exponent. For infinite words, alongside other results, we show that the asymptotic critical exponent grows at most by a constant factor (depending on the size of the alphabet) when mapped by an injective morphism. For both finite and infinite words, the binary case is better understood than the general case.

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