2021/02/05 by Rida Ait El Manssour, Manssour, Rida Ait El, Anna-Laura Sattelberger +1
Computer Science · Mathematics · #05E40 #12H05 (primary) #13P10 #52B20 (secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2102.03182
openalex publication_date 2021/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We link n-jets of the affine monomial scheme defined by xp to the stable set polytope of some perfect graph. We prove that, as p varies, the dimension of the coordinate ring of a certain subscheme of the scheme of n-jets as a ℂ-vector space is a polynomial of degree n+1, namely the Ehrhart polynomial of the stable set polytope of that graph. One main ingredient for our proof is a result of Zobnin who determined a differential Gröbner basis of the differential ideal generated by xp. We generalize Zobnin's result to the bivariate case. We study (m,n)-jets, a higher-dimensional analog of jets, and relate them to regular unimodular triangulations.