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.
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DOI: 10.5802/alco.6
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 = {http://archive.numdam.org/articles/10.5802/alco.6/} }
TY - JOUR AU - Baumeister, Barbara AU - Ladisch, Frieder TI - A property of the Birkhoff polytope JO - Algebraic Combinatorics PY - 2018 SP - 275 EP - 281 VL - 1 IS - 2 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.6/ DO - 10.5802/alco.6 LA - en ID - ALCO_2018__1_2_275_0 ER -
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. http://archive.numdam.org/articles/10.5802/alco.6/
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