# ALGEBRAIC COMBINATORICS

From generalized permutahedra to Grothendieck polynomials via flow polytopes
Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1197-1229.

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.

Revised: 2020-06-14
Accepted: 2020-06-17
Published online: 2020-10-12
DOI: https://doi.org/10.5802/alco.136
Classification: 05E05,  05C21,  52B12
Keywords: Flow polytopes, Grothendieck polynomials, generalized permutahedra.
@article{ALCO_2020__3_5_1197_0,
author = {M\'esz\'aros, Karola and St.~Dizier, Avery},
title = {From generalized permutahedra to Grothendieck polynomials via flow polytopes},
journal = {Algebraic Combinatorics},
publisher = {MathOA foundation},
volume = {3},
number = {5},
year = {2020},
pages = {1197-1229},
doi = {10.5802/alco.136},
language = {en},
url = {alco.centre-mersenne.org/item/ALCO_2020__3_5_1197_0/}
}
Mészáros, Karola; St. Dizier, Avery. From generalized permutahedra to Grothendieck polynomials via flow polytopes. Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1197-1229. doi : 10.5802/alco.136. https://alco.centre-mersenne.org/item/ALCO_2020__3_5_1197_0/

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