Mathematics Colloquia and Seminars

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Generalized permutohedra are defined as polytopes obtained from usual permutohedra by moving facets without passing vertices; or equivalently they are polytopes whose normal fan coarsens the Braid fan. We wanted to generalize this construction by allowing "passing some vertices". In joint work with Castillo, we consider a refinement of the Braid fan, called the nested Braid fan, and construct generalized nested permutohedra which have the nested Braid fan refining their normal fan. We extend many results on generalized permutohedra to this new family of polytopes.