2022/04/03 by Yining Hu, Hu, Yining, Alain Lasjaunias +1
Computer Science · Mathematics · #05A15 #11B50 #11B85 #11J70 #11T55 #11Y65 #Advanced Mathematical Identities #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2204.01068
openalex publication_date 2022/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Considering an arbitrary pair of distinct and non constant polynomials, a and b in \mathbbF2[t], we build a continued fraction in \mathbbF2((1/t)) whose partial quotients are only equal to a or b. In a previous work of the first author and Han (to appear in Acta Arithmetica), the authors considered two cases where the sequence of partial quotients represents in each case a famous and basic 2-automatic sequence, both defined in a similar way by morphisms. They could prove the algebraicity of the corresponding continued fractions for several pairs (a,b) in the first case (the Prouhet-Thue-Morse sequence) and gave the proof for a particular pair for the second case (the period-doubling sequence). Recently Bugeaud and Han (arXiv:2203.02213) proved the algebraicity for an arbitrary pair in the first case. Here we give a short proof for an arbitrary pair in the second case.