From generalized permutahedra to Grothendieck polynomials via flow polytopes

Karola Mészáros, Avery St. Dizier
2020 Algebraic Combinatorics  
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
more » ... nical, Tokcan, and Yong regarding the saturated Newton polytope property of Grothendieck polynomials.
doi:10.5802/alco.136 fatcat:q2c56txehjgedgm66zh3g5myly