From generalized permutahedra to Grothendieck polynomials via flow polytopes

@article{Mszros2017FromGP,
  title={From generalized permutahedra to Grothendieck polynomials via flow polytopes},
  author={K. M{\'e}sz{\'a}ros and Avery St. Dizier},
  journal={arXiv: Combinatorics},
  year={2017}
}
  • K. Mészáros, Avery St. Dizier
  • Published 2017
  • Mathematics
  • arXiv: 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… CONTINUE READING
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    SHOWING 1-10 OF 25 REFERENCES
    Newton polytopes and symmetric Grothendieck polynomials
    • 5
    • PDF
    Newton Polytopes in Algebraic Combinatorics
    • 18
    • Highly Influential
    • PDF
    Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra
    • 360
    • Highly Influential
    • PDF
    Faces of Generalized Permutohedra
    • 238
    • PDF
    Permutohedra, Associahedra, and Beyond
    • 380
    • Highly Influential
    • PDF
    Flow Polytopes and the Space of Diagonal Harmonics
    • 7
    • PDF