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arXiv · 2505.20102

On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence

Bill Allombert·Alain Lasjaunias
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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;-1}g 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.

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Bill Allombert, Alain Lasjaunias. 2025-05-26. On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence. https://arxiv.org/abs/2505.20102

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