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arXiv · 1705.02418

From generalized permutahedra to Grothendieck polynomials via flow polytopes

Karola Mészáros·Avery St. Dizier
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Abstract

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 Monical, Tokcan, and Yong regarding the saturated Newton polytope property of Grothendieck polynomials.

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Karola Mészáros, Avery St. Dizier. 2017-05-05. From generalized permutahedra to Grothendieck polynomials via flow polytopes. https://arxiv.org/abs/1705.02418

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