Special Events Seminar

The normalized volumes of certain root and flow polytopes equal the number of reduced pipedreams of certain permutations. Moreover, the Ehrhart series of the aforementioned polytopes can be expressed through specializations of Grothendieck polynomials. We explain these results by establishing a connection between triangulations of root and flow polytopes and the combinatorial expression of Grothendieck polynomials in terms of pipedreams. We then show that the Newton polytope of the Schubert polynomial for any permutation is a generalized permutahedron. Moreover, we prove the analogous statement for all homogeneous parts of Grothendieck polynomials of certain permutations. We achieve this by exploiting the connections between triangulations of root and flow polytopes and integer points of generalized permutahedra. This talk is based on joint works with Laura Escobar, Alex Fink and Avery St. Dizier. Speaker(s): Karola Meszaros (Cornell University)