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arXiv · 2312.16665

A small morphism giving Abelian repetition threshold less than 2

James D. Currie·Narad Rampersad
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Abstract

It is known that there are infinite words over finite alphabets with Abelian repetition threshold arbitrarily close to 1; however, the construction previously used involves huge alphabets. In this note we give a short cyclic morphism (length 13) over an 8-letter alphabet yielding an Abelian repetition threshold less than 1.8.

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James D. Currie, Narad Rampersad. 2023-12-27. A small morphism giving Abelian repetition threshold less than 2. https://arxiv.org/abs/2312.16665

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