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From generalized permutahedra to Grothendieck polynomials via flow polytopes
<span title="2020-10-12">2020</span>
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We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection considered (proven independently by Grinberg). We prove that left-degree polynomials encode integer points of generalized permutahedra. Using that certain left-degree polynomials are related to Grothendieck polynomials, we resolve special cases of conjectures by
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... nical, Tokcan, and Yong regarding the saturated Newton polytope property of Grothendieck polynomials.
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