Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal Square-free Words   A word is \emph{square-free} if it does not contain non-empty factors of the
form $XX$. In 1906 Thue proved that there exist arbitrarily long square-free
words over $3$-letter alphabet. We consider a new type of square-free words. A
square-free word is \emph{extremal} if it cannot be extended to a new
square-free word by inserting a single letter on arbitrary position. We prove
that there exist infinitely many extremal words over $3$-letter alphabet. Some
parts of our construction relies on computer verifications. We also pose some
related open problems.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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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: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph