ALGEBRAIC COMBINATORICS

no. 5
From generalized permutahedra to Grothendieck polynomials via flow polytopes
Mészáros, Karola1; St. Dizier, Avery1
1 Cornell University Department of Mathematics Ithaca NY 14853, USA.
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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.136
Classification: 05E05, 05C21, 52B12
Keywords: Flow polytopes, Grothendieck polynomials, generalized permutahedra.
Mészáros, Karola 1; St. Dizier, Avery 1

1 Cornell University Department of Mathematics Ithaca NY 14853, USA.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/articles/10.5802/alco.136/

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