Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weak Circular Repetition Threshold Over Large Alphabets   The repetition threshold for words on $n$ letters, denoted $\mbox{RT}(n)$, is
the infimum of the set of all $r$ such that there are arbitrarily long $r$-free
words over $n$ letters. A repetition threshold for circular words on $n$
letters can be defined in three natural ways, which gives rise to the weak,
intermediate, and strong circular repetition thresholds for $n$ letters,
denoted $\mbox{CRT}_{\mbox{W}}(n)$, $\mbox{CRT}_{\mbox{I}}(n)$, and
$\mbox{CRT}_{\mbox{S}}(n)$, respectively. Currie and the present authors
conjectured that
$\mbox{CRT}_{\mbox{I}}(n)=\mbox{CRT}_{\mbox{W}}(n)=\mbox{RT}(n)$ for all $n\geq
4$. We prove that $\mbox{CRT}_{\mbox{W}}(n)=\mbox{RT}(n)$ for all $n\geq 45$,
which confirms a weak version of this conjecture for all but finitely many
values of $n$.

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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex