The Birkhoff polytope is the convex hull of all permutation matrices in . We compute the combinatorial symmetry group of the Birkhoff polytope.
A representation polytope is the convex hull of some finite matrix group . 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.
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}, pages = {275--281}, publisher = {MathOA foundation}, volume = {1}, number = {2}, year = {2018}, doi = {10.5802/alco.6}, zbl = {06882342}, mrnumber = {3856525}, language = {en}, url = {https://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, pp. 275-281. doi : 10.5802/alco.6. https://alco.centre-mersenne.org/item/ALCO_2018__1_2_275_0/
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