Mapped Exponent and Asymptotic Critical Exponent of Words
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| Format: | Preprint |
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2025
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| _version_ | 1866918046096949248 |
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| author | Foster, Eva Saarela, Aleksi Vanhatalo, Aleksi |
| author_facet | Foster, Eva Saarela, Aleksi Vanhatalo, Aleksi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mapped Exponent and Asymptotic Critical Exponent of Words Foster, Eva Saarela, Aleksi Vanhatalo, Aleksi Combinatorics Formal Languages and Automata Theory 68R15 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. |
| title | Mapped Exponent and Asymptotic Critical Exponent of Words |
| topic | Combinatorics Formal Languages and Automata Theory 68R15 |
| url | https://arxiv.org/abs/2506.04091 |