Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A property of the Birkhoff polytope   The Birkhoff polytope $B_n$ is the convex hull of all $n\times n$ permutation
matrices in $\mathbb{R}^{n\times n}$. We compute the combinatorial symmetry
group of the Birkhoff polytope.
  A representation polytope is the convex hull of some finite matrix group
$G\leq \operatorname{GL}(d,\mathbb{R})$. We show that the group of permutation
matrices is essentially the only finite matrix group which yields a
representation polytope with the same face lattice as the Birkhoff polytope.

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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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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: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc