Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition theorem for invertible substitutions on three-letter
  alphabet   We shall characterize the structure of invertible substitutions on
three-letter alphabet. We show that any invertible substitution, after some
cyclic operation, can be written as a finite product of permutations and
Fibonacci's substitution. As a consequence, a matrix (of order 3 and with
non-negative integral coefficients) is the matrix of an invertible substitution
if and only if it is a finite product of non-negative elementary matrices.

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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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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: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph