ALGEBRAIC COMBINATORICS

no. 2

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 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.

Received:
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Accepted:
Published online:
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/articles/10.5802/alco.6/}
}
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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