Fixed Subpolytopes of the Permutahedron by Andrés R. Vindas Meléndez, Class of 1960s Speaker

Fixed Subpolytopes of the Permutahedron by Andrés R. Vindas Meléndez, University of Kentucky, Class of 1960s Speaker, Friday, April 26, 1-1:45 pm, Thompson Chemistry 206

Abstract:  Motivated by the generalization of Ehrhart theory with group actions, this project makes progress towards obtaining the equivariant Ehrhart theory of the permutahedron. The fixed subpolytopes of the permutahedron are the polytopes that are fixed by acting on the permutahedron by a permutation. We prove some general results about the fixed slices. In particular, we compute their dimension, show that they are combinatorially equivalent to permutahedra, provide hyperplane and vertex descriptions, and prove that they are zonotopes. Lastly, we obtain a formula for the volume of these fixed subpolytopes, which is a generalization of Richard Stanley’s result of the volume for the standard permutahedron. This is joint work with Federico Ardila (San Francisco State Unviersity), Mariel Supina (UC Berkeley), and Anna Schindler (North Seattle College).