A Property of the Birkhoff Polytope
نویسنده
چکیده
The Birkhoff polytope Bn is the convex hull of all n× n permutation matrices in Rn×n. We compute the combinatorial symmetry group of the Birkhoff polytope. A representation polytope is the convex hull of some finite matrix group G 6 GL(d,R). We show that the group of permutation matrices is essentially the only finite matrix group which yields a representation polytope with the face lattice of the Birkhoff polytope.
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