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Lilla Tóthmérész: h*-vectors of edge polytopes and symmetric edge polytopes

Time: Wed 2023-05-17 10.15 - 11.15

Video link: Meeting ID: 623 7437 7328

Participating: Lilla Tóthmérész (Eötvös University, Budapest)

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Abstract: Symmetric edge polytopes of graphs and edge polytopes of directed graphs are two classes of lattice polytopes whose \(h^*\)-polynomials have interesting properties and generalize important graph polynomials. I will talk about graph-theoretic formulas for these polynomials using activity statistics, and about the connection of the degree of the \(h^*\)-polynomial and the graph structure. We will also see that both results hold more generally in the case of regular oriented matroids. I will also mention some conjectures about the relationship of the \(h^*\)-polynomials for different orientations of a given graph. Joint work with Tamás Kálmán.