Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth rates of permutation classes: from countable to uncountable   We establish that there is an algebraic number $\xi\approx 2.30522$ such that
while there are uncountably many growth rates of permutation classes
arbitrarily close to $\xi,$ there are only countably many less than $\xi$.
Central to the proof are various structural notions regarding generalized grid
classes and a new property of permutation classes called concentration. The
classification of growth rates up to $\xi$ is completed in a subsequent paper.

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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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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: astro-ph
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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: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph