Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Growth of Grigorchuk's Group   In 1980 Rostislav Grigorchuk constructed a group $G$ of intermediate growth,
and later obtained the following estimates on its growth function:
$$e^{\sqrt{n}}\precsim\gamma(n)\precsim e^{n^\beta},$$ where
$\beta=\log_{32}(31)\approx0.991$. Using elementary methods we bring the upper
bound down to $\log(2)/\log(2/\eta)\approx0.767$, where $\eta\approx0.811$ is
the real root of the polynomial $X^3+X^2+X-2$.

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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat