Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian returns in Sturmian words   In this paper we study an abelian version of the notion of return word. Our
main result is a new characterization of Sturmian words via abelian returns.
Namely, we prove that a word is Sturmian if and only if each of its factors has
two or three abelian returns. In addition, we describe the structure of abelian
returns in Sturmian words, and discuss connections between abelian returns and
periodicity.

14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph