From generalized permutahedra to Grothendieck polynomials via flow polytopes
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 leftdegree polynomial, which we show is invariant of the dissection considered (proven independently by Grinberg). We prove that leftdegree polynomials encode integer points of generalized permutahedra. Using that certain leftdegree 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 arXiv:
 arXiv:1705.02418
 Bibcode:
 2017arXiv170502418M
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 33 pages