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arXiv · 2105.04004

Low dimensional flow polytopes and their toric ideals

Mátyás Domokos·Dániel Joó
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Abstract

The toric ideal of a $d$-dimensional flow polytope has an initial ideal generated by square-free monomials of degree at most $d$. 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.

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Mátyás Domokos, Dániel Joó. 2021-05-09. Low dimensional flow polytopes and their toric ideals. https://arxiv.org/abs/2105.04004

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