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arXiv · 1610.02077

A property of the Birkhoff polytope

Barbara Baumeister·Frieder Ladisch
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Abstract

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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Barbara Baumeister, Frieder Ladisch. 2017-10-13. A property of the Birkhoff polytope. https://doi.org/10.5802/alco.6

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