no. 2
A property of the Birkhoff polytope
Baumeister, Barbara1 ; Ladisch, Frieder2
1 Universität Bielefeld Postfach 100131 33501 Bielefeld Germany
2 Universität Rostock Institut für Mathematik 18051 Rostock Germany
Algebraic Combinatorics, Tome 1 (2018) no. 2, pp. 275-281.

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

A representation polytope is the convex hull of some finite matrix group G≤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 same face lattice as the Birkhoff polytope.

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DOI : 10.5802/alco.6
Classification : 52B15, 05E18, 20B25, 20C15, 52B05, 52B12
Mots clés : 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 
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Baumeister, Barbara; Ladisch, Frieder. A property of the Birkhoff polytope. Algebraic Combinatorics, Tome 1 (2018) no. 2, pp. 275-281. doi : 10.5802/alco.6. http://www.numdam.org/articles/10.5802/alco.6/

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