Math Colloquium: Ehrhart Theory and Partial Permutohedra

Presented by Dr. Erik Insko, Professor of Mathematics, Iowa State University.

In this talk, I will give a brief introduction to Ehrhart polynomials, which count the number of lattice points in a convex lattice polytope and also describe the polytope’s volume. Then I will define the partial permutohedron $P(m,n)$ and share how a simple sculpting idea has led to several new results and conjectures involving the volume and Ehrhart polynomial of the partial permutohedron $P(m,n)$ first defined and studied by Heuer and Striker in 2020. One goal of this talk is to be interesting and accessible to undergraduate and graduate students as well as faculty.