From generalized permutahedra to Grothendieck polynomials via flow polytopes

  title={From generalized permutahedra to Grothendieck polynomials via flow polytopes},
  author={K. M{\'e}sz{\'a}ros and Avery St. Dizier},
  journal={arXiv: Combinatorics},
  • 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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