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arXiv · 1605.00813

On certain recurrent and automatic sequences in finite fields

Alain Lasjaunias·Jia-Yan Yao
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Abstract

In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.

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Alain Lasjaunias, Jia-Yan Yao. 2016-05-03. On certain recurrent and automatic sequences in finite fields. https://arxiv.org/abs/1605.00813

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