Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The growth of torus link groups   Let $G$ be a finitely generated group with a finite generating set $S$. For
$g\in G$, let $l_S(g)$ be the length of the shortest word over $S$ representing
$g$. The growth series of $G$ with respect to $S$ is the series $A(t) =
\sum_{n=0}^\infty a_n t^n$, where $a_n$ is the number of elements of $G$ with
$l_S(g)=n$. If $A(t)$ can be expressed as a rational function of $t$, then $G$
is said to have a rational growth function.
  We calculate explicitly the rational growth functions of $(p,q)$-torus link
groups for any $p, q > 1.$ As an application, we show that their growth rates
are Perron numbers.

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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: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th