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{\bf Jessica Striker}
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{\bf The Alternating Sign Matrix Polytope}
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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.

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