On the 2-binomial complexity of the generalized Thue–Morse words

XT Lü, J Chen, ZX Wen, W Wu - Theoretical Computer Science, 2024 - Elsevier
In this paper, we study the 2-binomial complexity btm, 2 (n) of the generalized Thue–Morse
words tm over the alphabet {0, 1,…, m− 1} for every integer m≥ 3. By using boundary words …

Abelian closures of infinite binary words

S Puzynina, MA Whiteland - Journal of Combinatorial Theory, Series A, 2022 - Elsevier
Two finite words u and v are called Abelian equivalent if each letter occurs equally many
times in both u and v. The abelian closure A (x) of (the shift orbit closure of) an infinite word x …

On -abelian Equivalence and Generalized Lagrange Spectra

J Peltomäki, MA Whiteland - arxiv preprint arxiv:1809.09047, 2018 - arxiv.org
We study the set of $ k $-abelian critical exponents of all Sturmian words. It has been proven
that in the case $ k= 1$ this set coincides with the Lagrange spectrum. Thus the sets …

All growth rates of abelian exponents are attained by infinite binary words

J Peltomäki, MA Whiteland - 45th International Symposium on …, 2020 - drops.dagstuhl.de
We consider repetitions in infinite words by making a novel inquiry to the maximum eventual
growth rate of the exponents of abelian powers occurring in an infinite word. Given an …