Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian properties of Parry words   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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The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
20
The categories of this paper are: acc-phys