Mapped Exponent and Asymptotic Critical Exponent of Words

: Foster, Eva; Saarela, Aleksi; Vanhatalo, Aleksi

: Ko, Sang-Ki; Manea, Florin

: International Conference on Developments in Language Theory

Publisher: Springer Nature Switzerland

: 2025

: Lecture Notes in Computer Science

: Developments in Language Theory: 29th International Conference, DLT 2025, Seoul, South Korea, August 19–22, 2025, Proceedings

: 16036

: 244

: 260

: 978-3-032-01474-0

: 978-3-032-01475-7

: 0302-9743

: 1611-3349

DOI: https://doi.org/10.1007/978-3-032-01475-7_17

: https://doi.org/10.1007/978-3-032-01475-7_17

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. This is a shortened version of the full paper.