Matt Larson, Princeton University and Institute for Advanced Study

Abstract

Postnikov has shown that generalized permutohedra, polytopes whose edges are parallel to vectors of the form e_i - e_j, have remarkable formulas for their volumes and lattice point counts. Additionally, generalized permutohedra can be written as signed Minkowski sums of simplices. I will discuss a generalization of these results to signed generalized permutohedra, polytopes whose edges are parallel to vectors of the form e_i - e_j, e_i + e_j, or e_i. Joint work with Chris Eur, Alex Fink, and Hunter Spink.

See: https://sites.google.com/view/rutgersdmseminar