Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of rooted forests in circulant graphs   In this paper, we develop a new method to produce explicit formulas for the
number $f_{G}(n)$ of rooted spanning forests in the circulant graphs $
G=C_{n}(s_1,s_2,\ldots,s_k)$ and $ G=C_{2n}(s_1,s_2,\ldots,s_k,n).$ These
formulas are expressed through Chebyshev polynomials. We prove that in both
cases the number of rooted spanning forests can be represented in the form
$f_{G}(n)=p\,a(n)^2,$ where $a(n)$ is an integer sequence and $p$ is a
prescribed natural number depending on the parity of $n$. Finally, we find an
asymptotic formula for $f_{G}(n)$ through the Mahler measure of the associated
Laurent polynomial $P(z)=2k+1-\sum\limits_{i=1}^k(z^{s_i}+z^{-s_i}).$

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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat