Partial permutation and alternating sign matrix polytopes

Dylan Heuer, Jessica Striker

Published 2020-12-17Version 1

We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We use machinery developed in the study of sign matrix polytopes to determine the inequality descriptions, facet enumerations, and face lattices of these polytopes. We also study partial permutohedra that we show arise naturally as projections of these polytopes. We directly prove vertex and facet enumerations and also characterize the face lattices of partial permutohedra in terms of chains in the Boolean lattice.