2021/05/09 by M. Domokos, Domokos, Mátyás, Dániel Joó +1
Mathematics · #05E40 #13P10 #14M25 #15A39 #16G20 #52B20 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2105.04004
openalex publication_date 2021/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.