Talking About Combinatorial Objects Student Seminar: Generalized Permutahedra

Seminar | March 9 | 1-2 p.m. | 748 Evans Hall

 Mariel Supina, UC Berkeley

 Department of Mathematics

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.