On a family of continued fractions in Q((T¹)) associated to infinite binary words derived from the Thue-Morse sequence

2025/05/26 by Bill Allombert, Allombert, Bill, Alain Lasjaunias +1
Computer Science · Mathematics · #semigroups and automata theory #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2505.20102

Abstract

For each integer n > 1, we present an element in Q((T^-1)), having a power series expansion based on an infinite word W(n), over the alphabet +1;-1g and whose continued fraction expansion has a particular pattern which is explicitly described. The word W(1) is the Thue-Morse sequence and the following words are defined in a similar way.

Citations

• On a two-valued infinite sequence and a related continued fraction in Q((T^-1))
• On a two-valued sequence and related continued fractions in power series fields

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