Séminaire Lotharingien de Combinatoire, 85B.35 (2021), 12 pp.
Dylan Heuer and Jessica Striker
Partial Permutation and Alternating Sign Matrix Polytopes
Abstract.
We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions and number of facets of these polytopes. We also study partial permutohedra that we show arise naturally as projections of these polytopes. We enumerate vertices and facets and also characterize the face lattices of partial permutohedra in terms of chains in the Boolean lattice. Finally, we have a result and a conjecture on the volume of partial permutohedra when one parameter is fixed to be two.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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