Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequences with constant number of return words   An infinite word has the property $R_m$ if every factor has exactly $m$
return words. Vuillon showed that $R_2$ characterizes Sturmian words. We prove
that a word satisfies $R_m$ if its complexity function is $(m-1)n+1$ and if it
contains no weak bispecial factor. These conditions are necessary for $m=3$,
whereas for $m=4$ the complexity function need not be $3n+1$. New examples of
words satisfying $R_m$ are given by words related to digital expansions in real
bases.

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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg