A property of the Birkhoff polytope
Algebraic Combinatorics, Volume 1 (2018) no. 2, pp. 275-281.

The Birkhoff polytope B n is the convex hull of all n×n permutation matrices in n×n . We compute the combinatorial symmetry group of the Birkhoff polytope.

A representation polytope is the convex hull of some finite matrix group GGL(d,). 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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DOI: 10.5802/alco.6
Classification: 52B15,  05E18,  20B25,  20C15,  52B05,  52B12
Keywords: Birkhoff polytope, representation polytope, permutation polytope, combinatorial symmetry
Baumeister, Barbara 1; Ladisch, Frieder 2

1 Universität Bielefeld Postfach 100131 33501 Bielefeld Germany
2 Universität Rostock Institut für Mathematik 18051 Rostock Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Baumeister, Barbara; Ladisch, Frieder. A property of the Birkhoff polytope. Algebraic Combinatorics, Volume 1 (2018) no. 2, pp. 275-281. doi : 10.5802/alco.6. https://alco.centre-mersenne.org/articles/10.5802/alco.6/

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