A small morphism giving Abelian repetition threshold less than 2
Combinatorics
2023-12-29 v1 Formal Languages and Automata Theory
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.
Cite
@article{arxiv.2312.16665,
title = {A small morphism giving Abelian repetition threshold less than 2},
author = {James D. Currie and Narad Rampersad},
journal= {arXiv preprint arXiv:2312.16665},
year = {2023}
}
Comments
12 pages