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arXiv · 1406.1876

Abelian properties of Parry words

Ondřej Turek
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Abstract

Abelian complexity of a word $\mathbf{u}$ is a function that counts the number of pairwise non-abelian-equivalent factors of $\mathbf{u}$ of length $n$. We prove that for any $c$-balanced Parry word $\mathbf{u}$, the values of the abelian complexity function can be computed by a finite-state automaton. The proof is based on the notion of relative Parikh vectors. The approach works for any function $F(n)$ that can be expressed in terms of the set of relative Parikh vectors corresponding to the length $n$. For example, we show that the balance function of a $c$-balanced Parry word is computable by a finite-state automaton as well.

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Ondřej Turek. 2014-06-12. Abelian properties of Parry words. https://doi.org/10.1016/j.tcs.2014.11.024

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