JOURNAL ARTICLE

Algebraic Automatic Continued Fractions in Characteristic 2.

  • Published In: IMRN: International Mathematics Research Notices, 2024, v. 2024, n. 9. P. 7255 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Hu, Yining 3 of 3

Abstract

The article focuses on two families of automatic sequences, denoted |$\mathcal{P}$| and |$\mathcal{G}$|, that define algebraic continued fractions over the field |$\mathbb{F}_2$| of characteristic 2. The family |$\mathcal{P}$| generalizes the period-doubling sequence, while |$\mathcal{G}$| extends |$\mathcal{P}$| by including sequences formed via a specific binary operation involving periodic binary sequences. The main results establish that continued fractions defined by sequences in both families are algebraic over |$\mathbb{F}_2(A)$|, with degrees bounded by powers of two related to the period length, and that these sequences are |$2$|-automatic. The article also provides explicit constructions, matrix formulations, and proofs of convergence and algebraicity, extending previous work on Thue–Morse and period-doubling sequences in characteristic 2.

Additional Information

  • Source:IMRN: International Mathematics Research Notices. 2024/05, Vol. 2024, Issue 9, p7255
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:1073-7928
  • DOI:10.1093/imrn/rnad154
  • Accession Number:177084743
  • Copyright Statement:Copyright of IMRN: International Mathematics Research Notices is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.