Geodesic
The alternating sign matrix polytope
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We define the alternating sign matrix polytope as the convex hull of $n\times n$ alternating sign matrices and prove its equivalent description in terms of inequalities. This is analogous to the well known result of Birkhoff and von Neumann that the convex hull of the permutation matrices equals the set of all nonnegative doubly stochastic matrices. We count the facets and vertices of the alternating sign matrix polytope and describe its projection to the permutohedron as well as give a complete characterization of its face lattice in terms of modified square ice configurations. Furthermore we prove that the dimension of any face can be easily determined from this characterization.
DOI : 10.37236/130
Classification : 05C50, 52B05
Mots-clés : modified square ice configurations 
@article{10_37236_130,
     author = {Jessica Striker},
     title = {The alternating sign matrix polytope},
     journal = {The electronic journal of combinatorics},
     year = {2009},
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     number = {1},
     doi = {10.37236/130},
     zbl = {1226.05168},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/130/}
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Jessica Striker. The alternating sign matrix polytope. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/130

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