Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The extremal functions of classes of matroids of bounded branch-width   For a set of matroids $\mathcal{M}$, let $ex_\mathcal{M}(n)$ be the maximum
size of a simple rank-$n$ matroid in $\mathcal{M}$. We prove that, for any
finite field $\mathbb{F}$, if $\mathcal{M}$ is a minor-closed class of
$\mathbb{F}$-representable matroids of bounded branch-width, then $\lim_{n
\rightarrow \infty} ex_\mathcal{M}(n) / n$ exists and is a rational number,
$\Delta$. We also show that $ex_\mathcal{M}(n) - \Delta n$ is periodic when $n$
is sufficiently large and that $ex_\mathcal{M}$ is achieved by a subclass of
$\mathcal{M}$ of bounded path-width.

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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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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: dg-ga
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The categories of this paper are: physics
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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: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol