Szego Seminar: "Discrete Volume of Coxeter Permutahedra"

Speaker: Jodi McWhirter, Washington University in Saint Louis

Abstract: The discrete volume of an integral polytope, that is, the number of lattice points in the polytope, is given by the Ehrhart polynomial. The Ehrhart polynomials of the integral permutahedra of types A, B, C, and D have been calculated (Federico Ardila, Federico Castillo, and Michael Henley, 2015). However, it is often useful to work with these permutahedra when their center is at the origin, and in the case of type B and odd-dimension type A permutahedra, they become half-integral polytopes, and their Ehrhart quasipolynomials were previously unknown. Using signed graphs that arise from the generating vectors of each permutahedron, we are able to determine the information needed to compute the Ehrhart quasipolynomials.

Host: Nathan Wagner