Mariel Supina: Generalized permutahedra.


Abstract

The standard permutahedron is a polytope obtained by taking the convex hull of the orbit of the point (0, 1, ..., n) under the action of the symmetric group. Due to how it is constructed, the permutahedron contains a great deal of information about the symmetric group in its structure. I will present some interesting results about the permutahedron which will illustrate the link between this polytope and Coxeter systems of type A. I will also briefly introduce generalized permutahedra. Finally, I will discuss how to extend these definitions and results to other types.