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Hyperquadratic continued fractions and automatic sequences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2016Embargo end date: 01 Jan 2015 English Publisher:Elsevier BVJournal:Finite Fields and Their Applications, volume 40, pages 46-60 (issn: 1071-5797, Copyright policy )
Authors: Alain Lasjaunias; Jia-Yan Yao;

doi: 10.1016/j.ffa.2016.03.002 , 10.48550/arxiv.1509.09075

arXiv: 1509.09075

Hyperquadratic continued fractions and automatic sequences

Abstract

The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated by three families of examples and a counterexample.

Related Organizations
Keywords

Automata sequences, Continued fractions and generalizations, Mathematics - Number Theory, continued fractions, finite automata, power series over a finite field, automatic sequences, FOS: Mathematics, 11J70, 11T55, 11B85, Number Theory (math.NT), finite fields, Arithmetic theory of polynomial rings over finite fields

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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 4
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
Green
hybrid