Combinatorics Seminar: Ehrhart polynomials of generalized permutohedra from A to B

Abstract: I’ll show how to derive a formula for the Ehrhart polynomials for the type-$B$ generalized permutohedra, which offer a more concise alternative to the recent formula obtained by Eur, Fink, Larson, and Spink from their study of delta-matroids. My approach utilized some of the techniques and tools introduced around 20 years ago by Postnikov from his study of generalized type-$A$ permutohedra, a family of polytopes that interconnects with many mathematical concepts such as matroids, graphs, and Weyl groups. If time permits, I’ll discuss about some progress on computing their h-polynomials.

Host: Hsin-Chieh Liao