Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The topology of the external activity complex of a matroid   We prove that the external activity complex $\textrm{Act}_<(M)$ of a matroid
is shellable. In fact, we show that every linear extension of LasVergnas's
external/internal order $<_{ext/int}$ on $M$ provides a shelling of
$\textrm{Act}_<(M)$. We also show that every linear extension of LasVergnas's
internal order $<_{int}$ on $M$ provides a shelling of the independence complex
$IN(M)$. As a corollary, $\textrm{Act}_<(M)$ and $M$ have the same $h$-vector.
We prove that, after removing its cone points, the external activity complex is
contractible if $M$ contains $U_{3,1}$ as a minor, and a sphere otherwise.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org