Low dimensional flow polytopes and their toric ideals
Commutative Algebra
2021-05-11 v1 Algebraic Geometry
Abstract
The toric ideal of a -dimensional flow polytope has an initial ideal generated by square-free monomials of degree at most . The toric ideal of a flow polytope of dimension at most four has an initial ideal generated by square-free monomials of degree at most two, with the only exception of the four-dimensional Birkhoff polytope, whose toric ideal has an initial ideal generated by a square-free cubic monomial. The proof is based on a method to classify certain compressed flow polytopes, and a construction of a quadratic pulling triangulation of them. Along the way compressed flow polytopes are classified up to dimension four, and their Ehrhart polynomials are computed.
Cite
@article{arxiv.2105.04004,
title = {Low dimensional flow polytopes and their toric ideals},
author = {Mátyás Domokos and Dániel Joó},
journal= {arXiv preprint arXiv:2105.04004},
year = {2021}
}