A property of the Birkhoff polytope
Algebraic Combinatorics, Volume 1 (2018) no. 2, p. 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.
Received : 2017-09-20
Revised : 2017-10-12
Accepted : 2017-10-12
Published online : 2018-03-02
DOI : https://doi.org/10.5802/alco.6
Classification:  52B15,  05E18,  20B25,  20C15,  52B05,  52B12
Keywords: Birkhoff polytope, representation polytope, permutation polytope, combinatorial symmetry
@article{ALCO_2018__1_2_275_0,
     author = {Baumeister, Barbara and Ladisch, Frieder},
     title = {A property of the Birkhoff polytope},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {1},
     number = {2},
     year = {2018},
     pages = {275-281},
     doi = {10.5802/alco.6},
     zbl = {06882342},
     language = {en},
     url = {http://alco.centre-mersenne.org/item/ALCO_2018__1_2_275_0}
}
Baumeister, Barbara;Ladisch, Frieder. A property of the Birkhoff polytope. Algebraic Combinatorics, Volume 1 (2018) no. 2, p. 275-281. doi : 10.5802/alco.6. https://alco.centre-mersenne.org/item/ALCO_2018__1_2_275_0/

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