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Speaker: Matt Larson (Princeton/IAS)

Title: Signed permutohedra

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.