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arXiv · 2309.03180

Arithmetical subword complexity of automatic sequences

Jakub Konieczny·Clemens Müllner
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Abstract

We fully classify automatic sequences $a$ over a finite alphabet $\Omega$ with the property that each word over $\Omega$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal possible arithmetical subword complexity. More generally, we obtain an asymptotic formula for arithmetical (and even polynomial) subword complexity of a given automatic sequence $a$.

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Jakub Konieczny, Clemens Müllner. 2023-09-06. Arithmetical subword complexity of automatic sequences. https://arxiv.org/abs/2309.03180

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