Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sturm numbers and substitution invariance of 3iet words   In this paper, we give a necessary condition for an infinite word defined by
a non-degenerate interval exchange on three intervals (3iet word) to be
invariant by a substitution: a natural parameter associated to this word must
be a Sturm number. We deduce some algebraic consequences from this condition
concerning the incidence matrix of the associated substitution. As a by-product
of our proof, we give a combinatorial characterization of 3iet words.

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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg